Computational investigation of microperforated materials ...
Computational Investigation of Chemical Reactions ...
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Computational Investigation of Chemical Reactions: Exploring the Reactivity of Nickel Enoate and Fumarate Complexes and Radical Assistance in the Force-Enabled Bond Scission of Poly(Acrylic Acid) by Michael T. Robo A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Chemistry) in the University of Michigan 2020 Doctoral Committee: Professor John Montgomery, Co-Chair Associate Professor Paul M. Zimmerman, Co-Chair Professor Brian J. Love Professor Melanie S. Sanford Professor John P. Wolfe
Transcript of Computational Investigation of Chemical Reactions ...
Computational Investigation of Chemical Reactions: Exploring the
Reactivity of Nickel Enoate and Fumarate Complexes and Radical
Assistance in the Force-Enabled Bond Scission of Poly(Acrylic Acid)
by
Michael T. Robo
A dissertation submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
(Chemistry)
in the University of Michigan
2020
Doctoral Committee:
Professor John Montgomery, Co-Chair
Associate Professor Paul M. Zimmerman, Co-Chair
Professor Brian J. Love
Professor Melanie S. Sanford
Professor John P. Wolfe
ii
Dedication
To the brave and tireless healthcare workers involved in the ongoing COVID-19 pandemic.
iii
Acknowledgements
First, I would like to thank my parents, Jim Robo and Meredith Trim. They have provided me with
unending love and support for the entirety of my existence. My father pushed me early on to intern
at The Scripps Research Institute, and later encouraged me to take organic chemistry freshman
year of college. My mother has been similarly supportive, and helped me make my move to Ann
Arbor. I would also like to thank the many chemistry mentors that I have encountered over the
years, as they have guided me to where I am today. Early mentors include my high school
chemistry teacher Barbara Murphy, Roy Periana and the Periana lab, as well as Dan Weix, Michael
Prinsell, and the rest of the Weix lab. Pursuing a Ph.D. in chemistry can sometimes be a difficult
enterprise, and the positive experiences that they provided gave me the strength to pursue my
degree to completion.
I’ve had the pleasure of working with many collaborators over the years. Graduate students who
I’ve worked directly with include Alex Nett, Ellen Butler, Santiago Cañellas, Amie Frank on the
air-stable Ni(0) project, and Takunda Chazovachii, Danielle Fagnani, and Jessica Tami with
depolymerization. PIs I’ve worked with include Anne McNeil, Mark Banaszak Holl, and Neil
Marsh. The collaborations in the work reported here are enabled in part by the bounty of capable
students and PIs eager to collaborate that this department has to offer. Takunda Chazovachii in
particular has maintained a strong working relationship with me for a number of years.
The Procter and Gamble company has provided much of my financial support, and Dimitris Collias
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has worked with me on the P&G side of the poly(acrylic acid) project. P&G has also gifted me
with the opportunity to work there for a summer in 2017. Bruce Murch and Bill Laidig provided
me with a life-changing opportunity, and gave me the sense what industrial research is like.
The chemistry department has at the University of Michigan has been amazingly supportive over
the past 6 years, and I’m lucky to have the opportunity to work with two wonderful PIs. John
Montgomery was originally the sole chair of my committee, and he provided the support and
funding I needed for my first two years in the program. He was also more than accommodating
when it became clear that I was more suited for computational work. The investment in me from
him, Paul, and the department cannot be overstated. Paul Zimmerman, who became co-chair of
my committee in 2016, has been an excellent mentor. He has repeatedly amazed me with his deep
knowledge of disparate fields, and has been more than happy to provide valuable career advice.
Like John, Paul has shown a genuine care for his students, which has fostered in me a deep trust
in him. He was also instrumental in directing me towards my 2017 internship at Procter and
Gamble, as he recommended me for it based on confidence in me that I did not yet have in myself.
Finally, I would like to thank all of the friends that I’ve made in Ann Arbor over the years. My
coevals Aaron Proctor, Alonso Arguelles, and Grayson Ritch formed a core friend group that stood
the test of time. We put the effort in to regularly eat lunch and play games together, and it paid off
in the form of deep, lasting friendships. It seems unlikely to me that I’ll ever be able to forge
similar personal bonds like the ones formed among coevals in grad school. In addition to our group,
I’ve made many other friends, including Jacob Geri, Isaac Roles, Zach O’Keefe, and Cody Aldaz.
My experiences in grad school have been truly wonderful, and I’m forever grateful for the rich
social and intellectual life that Ann Arbor and the University of Michigan Department of
Chemistry have given me.
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Table of Contents
Dedication ....................................................................................................................................... ii
Acknowledgements ........................................................................................................................ iii
List of Figures .............................................................................................................................. viii
List of Tables ................................................................................................................................ xv
Abstract ........................................................................................................................................ xvi
Chapter 1: Introduction ................................................................................................................... 1
1.1 Using Computational Chemistry to Evaluate Chemical Reactions ....................................... 1
1.2 The Potential Energy Surface ................................................................................................ 3
1.3 Using the Critical States of the PES to Derive Reaction Thermodynamics and Kinetics .... 4
1.4 The Computational Evaluation of Chemical States .............................................................. 8
1.5 Identifying Transition States Using the Growing-String Method ....................................... 10
1.6 Outlook ................................................................................................................................ 12
Chapter 2: Computational Investigation of a Nickel-Catalyzed Three-Component Coupling
Reaction ........................................................................................................................................ 13
2.1 Background ......................................................................................................................... 13
2.2 Mechanistic Ambiguity in the Reductive [3+2] Cycloaddition of Enoates and Alkynes ... 15
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2.3 Determining and Evaluating the Possible Mechanisms of the Three-Component Coupling of
an Alkyne, Aldehyde, and Enoate ............................................................................................. 17
2.4 Determining the Fates of Complexes VI-A, V-B, and IV-C ............................................... 22
2.5 Considering the Reactivity of α-Substituted Enoates .......................................................... 24
2.6 Summary and Conclusions .................................................................................................. 28
Chapter 3: Elucidation of the Activation Mechanism of Air-Stable Nickel(0) Catalysts............. 29
Some of the material presented in this chapter has been reported in ACS Catalysis.56 ............ 29
3.1 Motivation for the Development of Air-Stable Nickel Pre-Catalysts ................................. 29
3.2 Investigating a Diverse Set of Nickel Fumarate Complexes ............................................... 32
3.3 Overturning the Original Hypothesis that Catalyst Activation Occurs via Dissociation .... 34
3.4 Investigating the Activation Sequence of BAC and IMes Fumarate Complexes ............... 37
3.5 Preliminary Results Towards the Development of an Air-Stable Nickel(0) BAC Catalyst 42
3.6 Summary, Conclusions, and Outlook .................................................................................. 45
Chapter 4: Synergistic Effects Between Radical Attack and Applied Force in the
Depolymerization of Poly(Acrylic Acid)...................................................................................... 46
4.1 The Potential Energy Surface Under Applied Force ........................................................... 46
4.2 Plastic Recycling Using Ultrasonic Depolymerization ....................................................... 50
4.3 Evaluating the Impact of the Weak Bond Effect Using a Morse Potential ......................... 54
4.4 Determining the Effect of Radical Abstraction on the Transition State of Bond Scission . 58
4.5 Determining the Effective Tensile Strength of PAA With and Without Radical Attack .... 60
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4.6 Geometric Distortions Due to Applied Force on the Reactant and Transition State .......... 63
4.7 Rationalizing why PATH-1 is More Responsive to Force Than PATH-2 .......................... 68
4.8 Conclusions ......................................................................................................................... 71
Chapter 5: Conclusions and Final Thoughts ................................................................................. 73
5.1 Research Summary .............................................................................................................. 73
5.2 Possible Future Directions for the Material Studied in This Work ..................................... 79
5.3 On the Frailty of Human Understanding ............................................................................. 81
5.4 On the Symbiosis Between Theory and Experiment .......................................................... 82
Appendix ....................................................................................................................................... 84
Bibliography ................................................................................................................................. 99
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List of Figures
Figure 1-1. (Left) A 3-dimensional potential energy surface. (Right) The same PES, represented
using a single reaction coordinate. The energies of the individual states are listed on the right-hand
side. ................................................................................................................................................. 3
Figure 1-2. Equilibrium constants (1) between states A and B and (2) for a chemical reaction.
Where: Keq is the equilibrium constant, ΔG is the change in free energy, R is the gas constant, and
T is the absolute temperature of the reaction. ................................................................................. 5
Figure 1-3. The Eyring equation gives the rate of a chemical reaction, such as the transformation
of A to B. Where: krxn is the rate of the reaction, κ is the transmission coefficient, kb is Boltzmann’s
constant, T is the absolute temperature of the system, h is Planck’s constant, and R is the gas
constant. κ is traditionally considered to be set to 1. ...................................................................... 5
Figure 1-4. A potential energy surface for the transformation of A to E. The largest barrier process
involves B transforming into D via TS-C....................................................................................... 6
Figure 1-5. An example catalytic transformation of reactants to products. Two cycles of the
process are shown, with the intermediates of the second cycle denoted with an apostrophe. ........ 7
Figure 1-6. The process of finding a transition state using the single-ended growing string method.
....................................................................................................................................................... 11
Figure 2-1. (Top) The Ni-mediated [3+2] cycloaddition of alkynyl enal 2-1. (Bottom Left)
Proposed mechanism of cyclization. (Bottom Right) Reported crystal structure of metallacycle 2-
2, taken from ref. 49. ..................................................................................................................... 14
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Figure 2-2. The mechanism of [3+2] cyclization of enoates and alkynes, as proposed by
Montgomery (ref. 50). The formation of a linear side product when 2-3 is used suggests that
formation of a 7-membered metallacycle is part of the catalytic cycle. ....................................... 15
Figure 2-3 The mechanism of [3+2] cyclization of enoates and alkynes, as proposed by Ogoshi
(ref. 51). NMR characterization of a nickel-enolate complex suggests the intermediacy of a ketene-
containing species ......................................................................................................................... 17
Figure 2-4. (Top) Both Ogoshi and Montgomery propose intermediates that are vulnerable to
electrophilic attack. (Bottom) The optimized conditions of the three-component coupling between
an alkyne, aldehyde, and enoate. These conditions are used as the basis for the computational study
....................................................................................................................................................... 18
Figure 2-5. The four possible mechanisms investigated in the studied reaction. ........................ 19
Figure 2-6. Isomerization of metallacycle I to η3-bound III-A, and direct insertion through
pathway D. Pathway D is denoted in purple. Energies are given in kcal/mol, with enthalpies listed
in parentheses. Energies are given in kcal/mol, with enthalpies listed in parentheses. ................ 20
Figure 2-7. Comparison of the aldol-first (paths A, B) and ketene-first (path C) mechanisms. Path
A (black): inner-sphere aldol-first mechanism; Path B (blue): outer-sphere aldol-first mechanism;
Path C (red): ketene-first mechanism. Energies are given in kcal/mol, with enthalpies listed in
parentheses. ................................................................................................................................... 21
Figure 2-8. Aldol addition in pathway C. Energies are given in kcal/mol, with enthalpies listed in
parentheses. ................................................................................................................................... 22
Figure 2-9. Carbocyclization in paths A and B. Energies are given in kcal/mol, with enthalpies
listed in parentheses. ..................................................................................................................... 23
x
Figure 2-10. Formation of a linear side product in the studied reaction using an α-substituted
enoate. The existence of such a product implicates formation of a 7-membered metallacycle
(boxed). ......................................................................................................................................... 24
Figure 2-11. The phenoxide moiety moves close to the α position (highlighted in gray) after ketene
elimination. Increasing the steric hinderance at that position is expected to destabilize complex
III-C. ............................................................................................................................................. 25
Figure 2-12. The potential energy surface for the first few steps of the [3+2] cycloaddition between
an alpha substituted enoate and an alkyne. Energies are given in kcal/mol, with enthalpies listed in
parentheses. ................................................................................................................................... 26
Figure 2-13. Comparing the barrier to ketene elimination with isomerization to the 7-embered
metallacycle for both the α- and β-substituted enoates. ................................................................ 27
Figure 3-1. Use of a pre-catalyst dramatically improves the yield of 3-1. Crystal structure taken
from reference 78. ......................................................................................................................... 30
Figure 3-2. (Top) Air-stable Ni(II) catalysts require a transmetallation reagent. (Middle) Tradeoffs
in the development of Ni(0) pre-catalysts. (Bottom) Molecular orbital diagram for the π
backbonding interaction. ............................................................................................................... 31
Figure 3-3. (Top) Different fumarate complexes were synthesized. (Bottom) The different
complexes were tested for their ability to catalyze a reductive coupling reaction. ...................... 33
Figure 3-4. Other complexes of fumarate A are not competent in reductive couplings. ............. 34
Figure 3-5. The mechanism of the reductive coupling reaction. Originally ligand dissociation was
believed to be the means of catalyst activation. ............................................................................ 34
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Figure 3-6. The relationship between the free energy of ligand exchange and the yield of 3-9 in
reductive coupling attempts with the corresponding catalyst. Computational details are included
in the appendix. ............................................................................................................................. 35
Figure 3-7. The isolation of products 3-12 and 3-13 from catalyst 3-8-A. .................................. 36
Figure 3-8. Possible activation mechanisms for complexes of fumarate A. ................................ 37
Figure 3-9. The initial steps of activation for IMes complex 3-8-A (blue and turquoise) and BAC
complex 3-10-A (red and pink). Dark colors (red, blue and black) represent aldol-first path A.
Light colors (pink, turquoise, and gray) represent ketene-first path B. Energies are given in
kcal/mol, with enthalpies listed in parentheses. Computational details are included in the appendix.
....................................................................................................................................................... 38
Figure 3-10. Pathway A of the activation of IMes catalyst 3-8-A, part 1. Energies are given in
kcal/mol, with enthalpies listed in parentheses. Computational details are included in the appendix.
....................................................................................................................................................... 40
Figure 3-11. Pathway A of the activation of IMes catalyst 3-8-A, part 2. Path Z details the possible
ester reduction reaction, and is shown in seafoam green. Energies are given in kcal/mol, with
enthalpies listed in parentheses. Computational details are included in the appendix. ................ 41
Figure 3-12. (Left) Complex BAC-IV-B can rearrange into carbonyl bound complex BAC-V-B.
(Right) A three-dimensional representation of complex BAC-V-B. ............................................ 42
Figure 3-13. Preliminary efforts towards developing a BAC fumarate catalyst. Fumarates that
favor metallacycle isomerization over ketene elimination are shown in blue. Fumarates where
metallacycle isomerization is within 1 kcal/mol or less than ketene elimination are shown in purple.
Listed energies are free energies in kcal/mol, and are relative to BAC-I (Figure 3-9).
Computational details are included in the appendix. .................................................................... 43
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Figure 4-1. The additive effect of applied force on the Morse potential. The distortion due to
applied force is greater at larger C-C bond distances. .................................................................. 46
Figure 4-2. Estimating the tensile of a C-C bond using the Morse method. ................................ 47
Figure 4-3. The expected effects of force according to the tilted potential energy surface model.
....................................................................................................................................................... 48
Figure 4-4. Recycling of polymers is enabled by ultrasonic depolymerization. .......................... 51
Figure 4-5. This chapter explores the synergistic interplay between radical attack and tensile force.
....................................................................................................................................................... 53
Figure 4-6. Model systems used in this study: Degradation of PAA through force alone (PATH-
1), and force in conjunction with radical attack (PATH-2). ......................................................... 55
Figure 4-7. Flowchart for evaluating tensile strength using the Morse method. The complete
procedure is described in the appendix. ........................................................................................ 55
Figure 4-8. Example three-dimensional representations of the tetramer (Right) and dimer+dimer
(Left) systems used for this study. These represent two of many snapshots used for this study. . 56
Figure 4-9. The effect of hydrogen atom abstraction on the tensile strength poly(acrylic acid).
Computational details are included in the appendix. .................................................................... 57
Figure 4-10. The relationship between enthalpy of activation and applied force on the polymer
chain. Computational details are included in the appendix. ......................................................... 59
Figure 4-11. Derivation of a relationship between enthalpy of activation (ΔH‡) and reaction half-
life (t1/2). Where: kb is Boltzmann’s constant, T is the reaction temperature, h is Planck’s constant,
R is the gas constant, ΔH‡ and ΔS‡ are the enthalpy and entropy of activation, ΔHpolym and ΔSpolym
are the enthalpy and entropy of polymerization, and Tc is the ceiling temperature of
polymerization. ............................................................................................................................. 61
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Figure 4-12. A contour plot of the effective tensile strength (E)FT of 1 and 2 assuming a Tc value
of 200 °C. ...................................................................................................................................... 62
Figure 4-13. Comparison of key geometries, which suggest that PATH-1 initial and TS structures
converge towards one another as forces increase, but PATH-2 structures do not. Explicit water
molecules are removed for clarity................................................................................................. 63
Figure 4-14. The effects of applied force on the end-to-end lengths in PATH-1 and PATH-2. 64
Figure 4-15. The effects of applied force on the scissile bond distances in PATH-1 and PATH-2.
....................................................................................................................................................... 66
Figure 4-16. The energetic contribution from applied force (ΔEAF) observed in PATH-1 and
PATH-2. The decrease in ΔH‡ with force in PATH-2 can be explained though the steady increase
in ΔEAF. ......................................................................................................................................... 67
Figure 4-17. Comparing the (relative) end-to-end and scissile bond distances of the starting and
TS structures in PATH-1 and PATH-2. The average end-to-end and scissile bond distances were
calculated within each reaction path. ............................................................................................ 68
Figure 4-18. Differences in the PES curvature of PATH-1 and PATH-2. ................................. 69
Figure 4-19. (Top) How the Morse and quartic potentials behave under applied force (Bottom
Left) Comparing the predicted TS energies of PATH-1 and PATH-2 using the example Morse
and quartic functions. The ratio of the change in energy with force (ESlope1 vs ESlope2) is very
close to the atomistic model. (Bottom Right) Comparing the displacement of the location of the
TS using the example Morse and quartic functions. The ratio of the change in displacement with
force at the last five data points (DispSlope1 vs DispSlope2) is consistent with the atomistic model.
....................................................................................................................................................... 70
xiv
Figure 5-1. A summary of Chapter 2. Two mechanisms for the three-component coupling reaction
were found to be plausible. The selectivity for a specific mechanism appears to be affected by the
placement of a methyl group at different positions of the enoate. ................................................ 75
Figure 5-2. (A) Original design strategy to develop an air-stable Ni(0) pre-catalyst. (B) No
Correlation between reaction yield and the free energy of ligand exchange was observed. (C) The
absence of such a correlation suggests that a fumarate consumption reaction must be active. .... 76
Figure 5-3. The insights gained from Chapter 2 explain why complex 3-8-A is active, but complex
3-10-A is not. The two complexes undergo activation through different mechanisms. 3-8-A goes
through an aldol-first mechanism, allowing for catalyst activation, but 3-10-A undergoes a ketene-
first activation, resulting in a stable ester-ligated complex. .......................................................... 77
Figure 5-4. A summary of Chapter 4. (A) Radical abstraction imparts a significant change in the
enthalpy of bond scission. (B) The barrier for bond scission in PATH-1 and PATH-2. (C)
Differences in the geometries of key states in PATH-1 and PATH-2. (D) We can explain the
differences in behavior between PATH-1 and PATH-2 to be due to the changes in the curvature
of the potential energy surfaces of the two processes. .................................................................. 78
Figure A-1. Model PAA systems used in this study. ................................................................... 88
Figure A-2. Flowchart for QM/MM optimization and bond scission. ......................................... 89
Figure A-3. Points where force is applied on compounds 1 and 2. The scissile bonds are shown in
red. ................................................................................................................................................ 91
Figure A-4. Flowchart for identifying the transition state of bond scission for compound 1. ..... 92
Figure A-5. Flowchart for identifying the transition state of bond scission for compound 2. ..... 92
xv
List of Tables
Table 4-1.The effective tensile strength of 1 and 2 calculated under different assumptions. ...... 61
Table A-1. Energetic values used to calculate relative energies in the activation pathway of IMes
catalyst 3-8-A. ............................................................................................................................... 85
Table A-2. Energetic values used to calculate relative energies in the activation pathway of BAC
catalyst 3-10-A. ............................................................................................................................. 86
Table A-3. Energetic values of small molecules used in the calculations of the activation pathways
of both 3-8-A and 3-10-A. ............................................................................................................ 86
Table A-4. Energetic values used in the comparison of ketene elimination with metallacycle
isomerization of BAC complexes using different fumarates. ....................................................... 87
Table A-5. Average calculated bond dissociation energy values in PATH-1 and PATH-2. ...... 95
Table A-6. Average calculated force constants in PATH-1 and PATH-2. .................................. 95
Table A-7. The average barriers for bond scission in PATH-1 and PATH-2. ............................ 95
Table A-8. The average end-to-end and scissile bond distances in 1, 2, TS-1, and TS-2. .......... 96
Table A-9. Parameters used for mathematical modeling in Chapter 4. ....................................... 97
Table A-10.The change in the transition state energy of the mathematical models of PATH-1 and
PATH-2. ....................................................................................................................................... 97
Table A-11. Displacement of the position of the transition state in the mathematical models of
PATH-1 and PATH-2. ................................................................................................................. 98
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Abstract
Computational chemistry has emerged as a powerful tool in identifying the key chemical states
that define the kinetics, thermodynamics, and the various selectivities of a chemical reaction. It
allows for a greater understanding of chemical processes by providing insights that would be
difficult to achieve through direct experimentation alone. Herein are described three examples
where computational analysis is used to provide insight into chemical reactions.
In Chapter 1, some fundamentals of computational research in chemistry is described. Topics
include the potential energy surface, the computational methods used for energy calculation, and
transition state finding using the growing string method. The tools described in this chapter are
used in the subsequent chapters.
Chapter 2 investigates the mechanism of a nickel-catalyzed [3+2] alkylative cycloaddition. Prior
experimental work has suggested multiple possible mechanisms, which are interrogated here
computationally. Two distinct mechanisms are found to be in a precarious balance with each other,
and small perturbations in the substrates used in the reaction are found to tilt the balance towards
one mechanism over the other. The findings from this chapter have implications for the mechanism
of [3+2] alkylative cycloadditions as a whole, including the activation process detailed in Chapter
3.
In Chapter 3, the activation process of air-stable nickel fumarate catalysts is studied. The original
hypothesis of fumarate dissociation as a mechanism of activation was overturned after
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computational analysis determined a fumarate consumption event must occur instead. These
findings inspired subsequent experimental work that isolated the products of fumarate dissociation,
and found that catalyst activation goes through a similar [3+2] alkylative cycloaddition detailed in
Chapter 2. Through this lens, the mechanisms of activation of active IMes catalyst and inactive
BAC catalyst are evaluated computationally, to provide a rationale for why one catalyst works and
the other does not. Using these insights, preliminary investigations towards improving the BAC
catalyst are performed.
Chapter 4 details the effect of radical attack on the tensile strength of poly(acrylic acid) (PAA).
Two different methods are used to determine how radical attack weakens the tensile strength of
the polymer backbone. Additionally, the effect of force in the radical-free and radical-abstracted
cases on the geometry of the starting structures and transition state of the species involved in bond
scission is observed. The different behaviors between the two regimes are attributed to the
differences in the curvature of their potential energy surfaces. The findings of this chapter carry
implications for the development of new depolymerization reactions.
Finally, Chapter 5 summarizes the work, and provides final thoughts on future directions. Elements
of this work are compared to the Gettier problem, and the symbiotic relationship between theorists
and experimentalists is discussed.
1
Chapter 1: Introduction
1.1 Using Computational Chemistry to Evaluate Chemical Reactions
In considering the development of a new chemical reaction, two conditions must hold true. Firstly,
the reaction must be thermodynamically feasible. This condition is satisfied if the entire chemical
process is exergonic, which means that the free energy of the final product is lower than the free
energy of the starting material. Secondly, the reaction must be kinetically feasible. While any
exergonic reaction is guaranteed to happen eventually, a kinetically feasible reaction will occur at
a rate that is useful to humans, and will also outcompete other potential pathways. The rate at
which a chemical reaction occurs is controlled by the energy of its highest energy state that occurs
during the chemical transformation.
To evaluate the kinetics and thermodynamics of a chemical reaction, therefore, all that is needed
to be done is to evaluate the energy of a few certain states. The challenge in computational
chemistry, then, is identifying the states that are relevant over the course of the reaction, and
accurately evaluating them. Fortunately, quantum chemical techniques such as density functional
theory (DFT) have emerged as a powerful tool to evaluate the energies of chemical structures.1
Additionally, recent development of transition-state finding and conformer-generating tools has
given computational chemists the ability to identify relevant chemical states at an unprecedented
pace.2
2
By leveraging these advancements, computational chemists are now in a position to provide useful
predictions, at a pace fast enough to keep up with experimental advancements. Chemical reactions
can often be challenging to characterize experimentally, and computational chemistry has the
advantage of being able to directly study the putative intermediates of a reaction. This contrasts
with the majority of experimental research in reaction development, which often focuses on the
inputs and outputs of a reaction, and can sometimes struggle to identify key intermediates.
This work describes a number of cases where computational chemistry is used to explain and
predict experimental results. Chapter 2 details the mechanism of a nickel-catalyzed three-
component coupling reaction. Previous work on related [3+2] reductive cycloadditions gave
conflicting evidence on what the active mechanism of the transformation could be, and the addition
of computational analysis provides clarity to the murky experimental picture. In Chapter 3, the
activation sequence of air-stable nickel(0) catalysts are examined. This chapter showcases the
ability of computational chemistry to provide useful predictions for the experimentalist, and uses
the knowledge gained from Chapter 2 as a framework for understanding catalyst activation. And
finally, in Chapter 4, the effects of hydrogen atom abstraction in the mechanochemical degradation
of poly(acrylic acid) are explored. Here, recently developed tools for transition state finding under
force are used, which allow for analysis of the differences in structure between bond scission under
force in the presence and absence of a radical on the polymer backbone.
The remainder of this chapter will provide a useful background for understanding the
computational analysis of chemical reactions. Topics to discuss include: defining the potential
energy surface, identifying and utilizing the key chemical states necessary to describe the
thermodynamics and kinetics of a reaction, computational methods to evaluate chemical states,
and modern transition state finding methods.
3
1.2 The Potential Energy Surface
Figure 1-1. (Left) A 3-dimensional potential energy surface. (Right) The same PES, represented using a single
reaction coordinate. The energies of the individual states are listed on the right-hand side.
For a given chemical system, there exists a multitude of possible arrangements of the atoms
involved in the system. If we imagine all of the arrangements, we can construct a hypersurface
existing in approximately 3N dimensions, with N being the number of atoms in the system. This
hypersurface is generally referred to as the “potential energy surface” (PES), and its contours are
what determines the mechanisms of chemical transformations. A simplified multi-dimensional
representation of such a surface is given on the left-hand side of Figure 1-1. In Figure 1-1, points
1, 2, and 3 are local minima on the surface, and which means they also represent chemical
intermediates. Intermediate 1 is capable of transitioning to 2 through the path containing TS-1,
and intermediate 2 can then transform into 3 through the path containing TS-2. Points TS-1 and
TS-2 are notable, as they are at saddle-points on the PES. The technical definition of a saddle point
is a point where the gradient equals zero, but is neither a local maximum or minimum. In the
context of analyzing the PES of a chemical system, saddle points are the highest energy point in
the lowest energy path between two local minima. The most probable path between two
4
intermediates will go through the saddle point, which in chemical terms is referred to as a transition
state, abbreviated as “TS” in this text.
While the PES provides a complete description of all possible atomic arrangements for a given
system, in practice, it is more useful to pictorially describe the PES along a single axis, as
represented on the right-hand side of Figure 1-1. This representation makes it easier to see the
energies of the different states involves, and simplifies the interpretation of the PES. By focusing
only on the critical states (intermediates and transition states), we can more easily determine the
kinetics and thermodynamics of a given chemical reaction.
1.3 Using the Critical States of the PES to Derive Reaction Thermodynamics and Kinetics
Determining the thermodynamics of a chemical reaction is a straightforward exercise. In looking
at the equilibrium between two states, the equilibrium constant is given by equation 1 (Figure 1-2).
Notably, as the difference in free energy (∆𝐺) grows larger, the equilibrium constant (𝐾𝑒𝑞) changes
at an exponential rate. In looking a unimolecular transformation, where species A transforms into
species B, the equilibrium constant is the expected ratio between the two states. Using the
relationship in equation 1, we can evaluate the thermodynamics of an entire chemical reaction
using equation 2 (Figure 1-2), where multiple reactants (R1, R2,…) are converted into multiple
products (P1, P2, …). Based off of equation 2, we can see that when a reaction is exergonic (∆𝐺 <
0), 𝐾𝑒𝑞 becomes larger than 1, indicating that if the reaction mixture were allowed to equilibrate,
the majority of the material would transform into the set of products. Additionally, given the
exponential nature of the equilibrium constant, a ∆𝐺 value of merely -10 kcal/mol would be
expected to equilibrate until the ratio of products to reactants exceeds 1,000,000 to 1.
5
Figure 1-2. Equilibrium constants (1) between states A and B and (2) for a chemical reaction. Where: Keq is the
equilibrium constant, ΔG is the change in free energy, R is the gas constant, and T is the absolute temperature of the
reaction.
While evaluating the thermodynamics a reaction requires the analysis of only the start and end
states, the kinetics of reaction is more difficult to compute. The rate at which a chemical reaction
progresses is given by the Eyring equation, shown in Figure 1-3. Under transition-state theory, the
transition state is considered to be in quasi-equilibrium with the reactants. Thus, as the Eyring
equation is based off of the equations for thermodynamic equilibrium, it shares many similar
features. In particular, under the Eyring equation, the difference in free energy between the reactant
and the transition state (∆𝐺‡) affects the rate at which the reaction can happen. As ∆𝐺‡ increases,
the rate of transformation decreases exponentially.
Figure 1-3. The Eyring equation gives the rate of a chemical reaction, such as the transformation of A to B. Where:
krxn is the rate of the reaction, κ is the transmission coefficient, kb is Boltzmann’s constant, T is the absolute
temperature of the system, h is Planck’s constant, and R is the gas constant. κ is traditionally considered to be set to
1.
However, a typical chemical reaction tends to involve multiple intermediates, with multiple
transition states where one intermediate transforms into another. In the multistep case, the time
6
that it takes for a unit of reactant to transform into a unit of product would be expected to be a
combination of the total time that it takes for all steps in the reaction to occur.3 However, this
picture can be greatly simplified by taking advantage of the exponential nature of the Eyring
equation. At room temperature, for every additional 1 kcal/mol increase in ∆𝐺‡, the corresponding
reaction takes about 5.4 times longer to occur. Thus, the largest overall ∆𝐺‡ ends up accounting
for the vast majority of the time needed for a chemical transformation to happen.3
Figure 1-4. A potential energy surface for the transformation of A to E. The largest barrier process involves B
transforming into D via TS-C.
Searching for the largest overall barrier is not a simple case of evaluating the energy of a transition
state relative to its prior intermediate. For instance, in Figure 1-4, in the transformation of A to E,
the largest barrier for the reaction is 16.0 units, measured between intermediate B and transition
state TS-C. The overall barrier is calculated to be 16.0 units as intermediate C is higher in energy
than B. That means, thermodynamically, only a small fraction of B will convert to C, and then, of
that small fraction, some of that material will convert to D through transition state TS-C. By
measuring the barrier from B to TS-C, we take into account the fact that conversion to C is a
thermodynamically unfavorable process. And as the Eyring equation is derived from the equations
7
in Figure 1-2, we can simply add the difference in energy between B and C to the barrier from C
to TS-C to derive an overall barrier for the transformation.3
A similar analysis can be performed on catalytic reactions.4–6 But, since catalytic reactions are by
nature cyclical, it’s possible that the catalytic cycle can initially form a very stable complex, and
then subsequently fail to “turn over”. The largest barrier can be found by looking at two contiguous
catalytic cycles, with the second cycle offset by the difference in energy between the reactants and
the products. With the new potential energy surface in hand, searching for the highest barrier can
proceed as normal. An example of this process is shown in Figure 1-5. In this example, the highest
barrier process involves intermediate B turning over the catalyst via TS-A’. Without considering
a second catalytic cycle, it would appear that the highest barrier process would be intermediate A
transforming into intermediate B, leading to an erroneous lower barrier, and a mistaken belief
about which states in the catalytic cycle have the greatest effect on catalyst turnover.
Figure 1-5. An example catalytic transformation of reactants to products. Two cycles of the process are shown, with
the intermediates of the second cycle denoted with an apostrophe.
8
1.4 The Computational Evaluation of Chemical States
Energy evaluation is a necessary component in the construction of a potential energy surface. The
main method used in this work is density functional theory (DFT). DFT is considered to have been
developed in 1964,1 when Hohenberg and Kohn proved that kinetic and potential energies of any
N-electron system can be described by a function of electron density (a so-called “density
functional”), implying that one could perfectly predict the properties of a system, if a perfect
density functional was in hand.7 The following year, Kohn and Sham demonstrated that a density
functional that treats all of the electrons as non-interacting accounts for the bulk of the total energy,
meaning that only the small effect of electron interaction, termed the “exchange-correlation
energy” needs to be determined to obtain an exact result.8
By avoiding the direct computation of electron-electron interactions, DFT scales at a relatively
low cost (N3 , where N is the number of electrons), which compares favorably with wavefunction
based methods (N4-10).9 While in principle, DFT can deliver perfect accuracy with a perfect
functional that describes the exchange-correlation energy, in practice, no such functional exists,
and the exchange-correlation energy is approximated. The approaches towards approximating the
exchange-correlation energy are diverse and numerous, and this had led to the development of a
large menagerie DFT functionals, with differing accuracies and computational costs.10 In this work
the ωB97X-D311 functional is used in Chapters 2 and 3, and the B3LYP12 functional is used in
Chapter 4. While the errors calculated DFT functionals are dependent on the benchmarking set
used, they provide a useful sense of the accuracy of the functional. In interpreting the
computational results of this work, an error of approximately 2 kcal/mol for ωB97X-D3, and
approximately 5 kcal/mol for B3LYP, should be considered.13
9
Another consideration in the accuracy of DFT is the choice of basis set for the calculation. While
a DFT functional ultimately defines the density of electrons a given chemical system, the basis set
describes the orbitals within which the electrons reside. The choice of which orbitals to define, and
how to define them, is another factor that can influence the cost and accuracy of a calculation. In
general, “double zeta” basis sets (where two functions are used to describe each atomic orbital)
are used for processes such as geometry optimization or transition-state finding, where many
iterative energy and gradient calculations are performed, and the more computationally expensive
“triple zeta” basis sets (three functions per atomic orbital) are used for accurate energy calculations
on an optimized structure.14
Ab initio methods such as DFT only require the choice of basis set, functional, and the cartesian
coordinates for the atoms in the chemical system to be studied. Their simplicity makes them well
suited to investigate structures where features such as bond lengths, angles, and torsions are
ambiguous, such as in most transition states or metal complexes. However, arriving at those
features from first principles is computationally taxing, and in our hands, DFT calculations on
systems larger than 200 atoms are too slow to be of use. In molecular mechanics (MM), the
parameters that can define features such as bond lengths, angles, and torsions are determined
beforehand, often fit to quantum chemical calculations. Using these parameters to calculate the
energy of the system results in a speed up of multiple orders of magnitude. In general, molecular
mechanics is attractive for lager systems, and is often used to simulate proteins or molecules in the
condensed phase.15
As molecular mechanics is a good choice for the simulation of large condensed phases, and
quantum methods such as DFT is a good choice for the simulation of transition states, a method
that uses both quantum and molecular mechanical techniques may be best suited for the study of
10
transition states within a large system. In QM/MM, a portion of a chemical system is treated using
a quantum method such as DFT, MP2, or semi-empirical methods, and the remainder of the system
is treated using molecular mechanics.16 In Chapter 4 of this work, a QM/MM system is used with
CHARMM2717,18 molecular mechanics parameters, in conjunction with DFT using the B3LYP
functional with the 6-31G* basis, using an electronic embedding system.19
1.5 Identifying Transition States Using the Growing-String Method
While the structure of chemical intermediates only requires following the analytic first derivative
to find a local minimum,20 transition state finding is more difficult, as it is neither a local maximum
or minimum on the PES, so a strategy of only following the gradient cannot be used. Fortunately,
a number of tools have been developed for transition state searching. These include the linear
synchronous transit method,21 the nudged elastic band method,22,23 and many others. In the
Zimmerman group, a growing string method (GSM) using an internal coordinate system has been
developed,24–26 and is the method of choice in this work for the purposes of identifying transition
states. The chief advantages of using GSM is that it allows for the user to be ignorant of the
potential structure of the transition state, and, in the case of single-ended GSM, also be ignorant
of the potential structure of the product.
The process for single-ended GSM26 is detailed in Figure 1-6. In the example reaction, the SN2
addition of thiolate to methyl bromide, the user defines the bonds that they would like to add and
break (Top Left). The add and break moves are then interpreted to define the R-P (reactant-
product) tangent, a vector on the potential energy surface that dictates the general direction to find
a transition state (Top Right). In the direction of the R-P tangent, a new structure (referred to as a
node) can be generated (Figure 1-6, 1). This node can then be optimized in all directions except
along the R-P tangent (2). From the optimized node, a second node can be generated along the
11
Figure 1-6. The process of finding a transition state using the single-ended growing string method.
12
R-P tangent (3), and then optimized again (4), creating a string of nodes. This process can be
repeated, until the nodes begin to decrease in energy, indicating that a saddle point has been crossed
(5). Finally, to identify the transition state, the nodes along the growing string are optimized again,
and then the highest-energy node is optimized to a transition state using a climbing image search
(6).25
1.6 Outlook
Despite rough complexity and high dimensionality of the PES, a reaction can be evaluated using
only a handful of points on the hypersurface. The thermodynamics of the entire process can be
determined by comparing the free energy of all of the reactants compared to all of the products.
The kinetics of a reaction can be determined by the observing the largest possible climb in energy
between an intermediate and a transition state that occurs in the reaction. Even though in theory,
the energetics of only four states need to be evaluated to have an understanding of the kinetics and
thermodynamics of a reaction, in practice, more states are typically evaluated, if only to be certain
that those processes are possible. These techniques and concepts will be used in the coming
chapters to evaluate the chemical process of a three-component coupling reaction, the activation
sequence of an air-stable nickel(0) catalyst, and the depolymerization of poly(acrylic acid)
13
Chapter 2: Computational Investigation of a Nickel-Catalyzed
Three-Component Coupling Reaction
The content in this chapter has been published in the Journal of Organic Chemistry.27
2.1 Background
Five-membered carbocycles are a common structural motif in biology, which has resulted in the
development of a rich body of literature on their synthesis.28–33 Within that body of research,
countless strategies for 5-membered ring formation have been developed, including the Nazarov
cyclization,32 ring-expansion reactions,34 ring-closing metathesis,35 radical cyclizations,36
intramolecular nucleophilic attack,33 cross-couplings,37 or cycloisomerization reactions.33 In
addition to these listed methods, cycloaddition reactions, in which a ring is formed from multiple
separate components, have also been developed. These can include [3+2] cycloadditions, [2+2+1]
cycloadditions, and [4+1] cycloadditions.33
[3+2] cycloadditions in particular have developed into a powerful synthetic method, due to their
potential for chemo-, regio-, diasterio- and enantioselectivity.28 These transformations can be
accomplished through the use of donor-acceptor cyclopropanes,38 vinyl carbenoid additions,28
allyl- or allenylsilane additions,39 or ylide additions.40 Reductive metal-promoted [3+2]
cycloadditions have also represented a viable strategy towards cyclopentane formation. A number
of processes have been developed to couple readily available reagents such as alkynes and α,β-
unsaturated carbonyl compounds. In such processes, stoichiometric amounts of nickel,41
14
titanium,42,43 iron,44,45 or cobalt46 metallacycles are formed, which can then then collapse into a 5-
membered ring after protonation or alkylation (Figure 2-1).
Figure 2-1. (Top) The Ni-mediated [3+2] cycloaddition of alkynyl enal 2-1. (Bottom Left) Proposed mechanism of
cyclization. (Bottom Right) Reported crystal structure of metallacycle 2-2, taken from ref. 49.
The Montgomery group has a long history of using nickel metallacycles in cycloaddition
reactions.41,47 The group first reported a nickel-mediated [3+2] reductive cyclization in 2000,48
combining alkynyl enal 2-1 with stochiometric Ni(COD)2 and TMEDA, to create 7-membered
metallacycle 2-2, which can then be quenched with water, methyl iodide, or benzaldehyde to create
15
a cyclopentenone (Figure 2-1). This transformation was though to occur via initial nucleophilic
attack by the enolate moiety in 2-2, followed by subsequent nucleophilic attack on the resulting
aldehyde by the nickel-vinyl species. Metallacycle 2-2 was later directly isolated, and its structure
confirmed by X-ray crystallography.49
2.2 Mechanistic Ambiguity in the Reductive [3+2] Cycloaddition of Enoates and Alkynes
Figure 2-2. The mechanism of [3+2] cyclization of enoates and alkynes, as proposed by Montgomery (ref. 50). The
formation of a linear side product when 2-3 is used suggests that formation of a 7-membered metallacycle is part of
the catalytic cycle.
16
The stoichiometric reactions detailed in Figure 2-1 paved the way for methods catalytic in nickel
to be developed. In 2011, Montgomery50 reported catalytic, intramolecular [3+2] cycloaddition
reactions of enals with alkynes and of enoates with alkynes. In a separate, concurrent report,
Ogoshi51 also detailed the cycloaddition of enoates and alkynes, using isopropanol as a reductant.
Remarkably, even though both reports detail similar transformation, and both use a nickel catalyst
with a strong σ-donor ligand, Montgomery and Ogoshi attribute the formation of the [3+2]
cycloadduct to separate mechanisms, and both authors provide compelling evidence to support
their mechanistic proposals.
In Montgomery’s publication, the proposed mechanism of cyclopentenone formation involves the
cyclization of the enoate and alkyne, and then subsequent isomerization to a 7-membered
metallacycle (Figure 2-2).50 The resulting metallacycle can be protonated to form a nickel species
with a π-bound carbonyl, and then undergo carbocyclization, followed by subsequent alkoxide
extrusion to yield the desired cyclopentenone product. Support for this mechanism stems from the
observation of linear side products from the attempted cycloadditions of enoate 2-3, where the
ester moiety is kept intact. These observed side products are comparable to previous work52,53 from
the group in which enals and enones are reductively coupled with alkynes to create similar
products. Their formation is attributed to the intermediacy of a 7-membered metallacycle, similar
to the previously reported 2-2.
However, in Ogoshi’s report, a different mechanistic picture is painted (Figure 2-3).51 In that
report, it was posited that after the enoate and alkyne cyclize, rather than isomerize to a 7-
membered metallacycle, the complex instead undergoes phenoxide elimination to form a ketene
complex. The ketene complex can then undergo carbocyclization to yield a nickel enolate species
that can then be protonated off. Catalyst regeneration occurs via β-hydride elimination of the
17
resulting nickel-isopropoxide complex. To support this mechanistic proposal, Ogoshi also reports
the NMR characterization of the nickel enolate species with an IPr ligand, which is formed quickly
from starting materials in the absence of isopropanol, and quickly decays into product once
isopropanol is added.
Figure 2-3 The mechanism of [3+2] cyclization of enoates and alkynes, as proposed by Ogoshi (ref. 51). NMR
characterization of a nickel-enolate complex suggests the intermediacy of a ketene-containing species
2.3 Determining and Evaluating the Possible Mechanisms of the Three-Component Coupling
of an Alkyne, Aldehyde, and Enoate
As both Montgomery and Ogoshi provide concrete support for their proposed mechanisms, it
seems unlikely that only one mechanism is active in the [3+2] cycloaddition between an enoate
18
alkyne. Rather, it is more likely that multiple mechanisms are possible, and small changes in the
reactant conditions can push the reaction to favor one mechanism over another. However, despite
the difference between the two proposed mechanisms, in both cases, catalyst turnover is enabled
by the protonation of a nickel enolate species with an alcohol. If the alcohol was removed from
the reaction conditions, and replaced by an electrophilic carbon, it could be possible to form an
additional carbon-carbon bond in the process (Figure 2-4, top).
Figure 2-4. (Top) Both Ogoshi and Montgomery propose intermediates that are vulnerable to electrophilic attack.
(Bottom) The optimized conditions of the three-component coupling between an alkyne, aldehyde, and enoate. These
conditions are used as the basis for the computational study
Through careful optimization of reaction conditions, Montgomery group student Aireal Jenkins
was able to realize a catalytic, three-component coupling reaction by incorporating an aldol
reaction in with the [3+2] reductive cycloaddition of an enoate and alkyne (Figure 2-4, bottom).
With a working reaction in hand, it was at this point that computational analysis was requested.
19
The goals of the computational study were to clarify the mechanism through which the three-
component coupling occurs. While multiple sets of conditions were developed for the reaction,
including using either phosphine ligand PBu3 or NHC (N-heterocyclic carbene) ligand IMes, the
conditions listed in Figure 2-4 were chosen for computational study due to the popularity of NHC
ligands in the more recent reductive coupling work by the Montgomery group.54
Figure 2-5. The four possible mechanisms investigated in the studied reaction.
Based on the mechanisms proposed by Montgomery50 and Ogoshi51 in their respective reports, as
well as from reviewer input in the publication of the data in this chapter, four possible mechanisms
for the three-component coupling can be envisioned (Figure 2-5). Pathways A and B are based on
the mechanistic proposal of Montgomery, with the intermediacy of a 7-membered metallacycle.
In these so-called “aldol-first” pathways, the aldol addition occurs prior to carbocyclization. In
pathway A, the unit of aldehyde coordinates directly to the metal center, allowing for an inner-
20
sphere aldol addition. In pathway B, the aldol addition occurs in an outer-sphere process without
any prior aldehyde coordination. Pathway C is a “ketene first” mechanism based off of the
mechanistic proposal of Ogoshi, where carbocyclization occurs prior to aldol addition. And in the
lass possible mechanism, pathway D, a coordinated aldehyde inserts directly into the 5-membered
metallacycle, based off of reviewer comments during publication review.
Figure 2-6. Isomerization of metallacycle I to η3-bound III-A, and direct insertion through pathway D. Pathway D is
denoted in purple. Energies are given in kcal/mol, with enthalpies listed in parentheses. Energies are given in
kcal/mol, with enthalpies listed in parentheses.
As all four investigated mechanisms begin with the oxidative cyclization of the enoate and alkyne,
metallacycle I (Figure 2-6) is used as the reference structure. In order to isomerize to the 7-
membered metallacycle, I must first isomerize to η3 intermediate III-A, via rotation (TS-I) to
isomer II, followed by carbonyl binding (TS-II-A) to yield III-A. Additionally, it is also possible
21
for benzaldehyde to coordinate to metallacycle I to yield complex II-D, which can then directly
insert (TS-II-D), to create tetracoordinate species VI-A.
Figure 2-7. Comparison of the aldol-first (paths A, B) and ketene-first (path C) mechanisms. Path A (black): inner-
sphere aldol-first mechanism; Path B (blue): outer-sphere aldol-first mechanism; Path C (red): ketene-first
mechanism. Energies are given in kcal/mol, with enthalpies listed in parentheses.
Using structure I as an energy reference, the remaining pathways (A, B, and C) are also examined
(Figure 2-7). Complex II acts as the branching point between aldol-first mechanisms A and B, and
ketene-first mechanism C. Species II can isomerize to III-A (Figure 2-6), and then isomerize again
to 7-membered metallacycle IV-A (TS-III-A). Here paths A and B separate. In path A,
benzaldehyde coordinates to IV-A to create V-A, which then undergoes inner-sphere aldol
addition (TS-V-A) to yield tetracoordinate species VI-A. In path B, a benzaldehyde-BEt3 complex
adds to IV-A (TS-IV-B), to yield V-B.
22
In path C, rather than isomerize to III-A, species II instead undergoes ketene elimination (TS-II-
C) to create ketene complex III-C. Complex III-C then undergoes carbocyclization (TS-III-C),
to yield nickel enolate IV-C. As the formation of IV-C is highly exergonic (-28.5 kcal/mol relative
to I), its formation is expected to be irreversible under the studied conditions. Furthermore, the
relatively low barrier for the formation of IV-C (highest barrier process is TS-II-C, 15.0 kcal/mol)
compared to the barrier for isomerization to a 7-membered metallacycle (TS-III-A, 16.4 kcal/mol),
or the barrier for direct insertion of an aldehyde (TS-II-D, 25.6 kcal/mol), means that the formation
of IV-C in pathway C is expected to outcompete pathways A, B, and D. Based off of the potential
energy surfaces detailed in Figures 2-6, and 2-7, therefore, it was found that ketene-first pathway
C is expected to be the dominant reaction pathway in the studied reaction.
2.4 Determining the Fates of Complexes VI-A, V-B, and IV-C
Figure 2-8. Aldol addition in pathway C. Energies are given in kcal/mol, with enthalpies listed in parentheses.
After carbocyclization to form intermediate IV-C, the aldol addition in pathway C is expected to
occur through an inner-sphere pathway (Figure 2-8). Coordination of benzaldehyde to IV-C yields
23
complex V-C, which can then isomerize to O-bound enolate species VI-C. The O-bound enolate
can then engage in rapid aldol addition (TS-VI-C), to yield aldol adduct VII-C. After aldol
addition, catalyst turnover can then be accomplished by reaction of VII-C with triethylboron.
Figure 2-9. Carbocyclization in paths A and B. Energies are given in kcal/mol, with enthalpies listed in parentheses.
Though Figure 2-7 shows that ketene-first pathway C is expected to be the major pathway in the
three-component coupling of an alkyne, aldehyde, and enoate, the evaluation of pathways A, and
B is still beneficial (Figure 2-9). In particular, evaluating the carbocyclization of paths A and B
distinguishes between those reaction pathways being viable mechanisms that might emerge under
perturbation of the reaction conditions, or being unfeasible mechanisms that should not be
24
considered in the future. Both intermediates VI-A and V-B eventually converge to ethyl-nickel
species VIII-A. In path A, coordination of triethylboron to VI-A yields complex VII-A. This
species can then transfer an ethyl group to the nickel center to create VIII-A. In pathway B,
isomerization to VII-A (TS-V-B) is a higher barrier process compared to direct ethyl transfer (TS-
VI-B) to yield complex VIII-A. After formation of VIII-A, carbocyclization (TS-VIII-A) can
proceed, resulting in carbocycle IX-A, which is expected to be capable of extruding a unit of
phenoxide, and ultimately turning over the nickel catalyst.
While pathway C is expected to be the dominant pathway for catalyst activation, pathway A has
an overall barrier that is only slightly higher in energy. The highest overall barrier for path A is
nickel ethylation (TS-VII-A, Figure 2-9) at 18.5 kcal/mol, 2.5 kcal/mol shy of the largest net
barrier for pathway C prior to carbocyclization (TS-II-C, Figure 2-7). Pathways B and D both
have much larger overall barriers (path B: TS-VI-B, 24.5 kcal/mol, path D: TS-II-D, 25.6
kcal/mol), and can be considered to be much less feasible reactions compared to paths A and C.
2.5 Considering the Reactivity of α-Substituted Enoates
Figure 2-10. Formation of a linear side product in the studied reaction using an α-substituted enoate. The existence
of such a product implicates formation of a 7-membered metallacycle (boxed).
25
The potential energy surfaces shown in Sections 2.3 and 2.4 detail a three-component coupling
reaction involving a β-substituted enoate. However, it is already known that α-substituted enoate
2-3 is capable of producing a linear side product, which implicates the existence of a 7-membered
metallacycle (Figure 2-2). Furthermore, in the development of the three-component coupling
reaction, Aireal Jenkins was also able to identify the formation of a linear product using 2-3 (Figure
2-10). These points of evidence suggest that the mechanism of the reductive [3+2] cycloaddition
between an enoate and an alkyne, and by extension, the three-component coupling reaction
studied, go through different mechanisms, depending on the substitution pattern of the enoate.
Figure 2-11. The phenoxide moiety moves close to the α position (highlighted in gray) after ketene elimination.
Increasing the steric hinderance at that position is expected to destabilize complex III-C.
Closer examination of the geometry of the ketene elimination product (III-C, Figure 2-7) suggests
a rationale for why such a perturbation in mechanism might take place. Figure 2-11 details the
geometry of III-C. Notably, after eliminating the phenoxide moiety to form a ketene, the
phenoxide in the resulting complex is oriented close (2.3 Å) to the hydrogen in the α position
(highlighted in gray). If the α position were to become more sterically crowded, it could be
imagined that ketene elimination would become more difficult.
26
Figure 2-12. The potential energy surface for the first few steps of the [3+2] cycloaddition between an alpha
substituted enoate and an alkyne. Energies are given in kcal/mol, with enthalpies listed in parentheses.
Based off of this observation, the early stages of metallacycle isomerization were investigated
computationally for the three-component coupling reaction involving starting enoate 2-3. The
potential energy surface for these initial steps are shown in Figure 2-12. After isomerization of
metallacycle α-I to rotamer α-II, the complex can either undergo ketene elimination to form
complex α-III-C, or isomerization to yield 7-membered metallacycle α-IV-A. Unlike the reaction
of a β-substituted enolate, metallacycle formation is expected to outcompete ketene elimination
when an α-substituted enoate is used, as both the of the transition states associated with the
formation of the metallacycle (α-TS-II-A, 15.3 kcal/mol and α-TS-III-A, 17.2 kcal/mol) are lower
in energy than the transition state for ketene elimination (α-TS-II-C, 17.8 kcal/mol).
The differences between the potential energy surfaces of the α- and β-substituted enoates can be
more clearly seen if the respective surfaces are lined up next to each other (Figure 2-13). While
27
changing from a β-substituted enoate to an α-substituted one increases the barrier for isomerization
to the 7-membered metallacycle by 0.8 kcal/mol (TS-III-A vs α-TS-III-A), the barrier for ketene
elimination increases by a much larger amount, 2.8 kcal/mol (TS-II-C vs α-TS-II-C). The 2.0
kcal/mol net swing in energy means that ketene elimination changes from being favored by 1.4
kcal/mol to being disfavored by 0.6 kcal/mol, relative to isomerization to the 7-membered
metallacycle.
Figure 2-13. Comparing the barrier to ketene elimination with isomerization to the 7-embered metallacycle for both
the α- and β-substituted enoates.
Even though metallacycle formation is now capable of outcompeting ketene elimination, this does
not guarantee that the three-component coupling of 2-3 goes through an aldol-first type
mechanism. It is possible that ketene elimination could outcompete steps further along the
28
potential energy surface of the aldol-first path, such as triethylboron addition. However, the change
does explain how linear side products that necessitate the formation of a 7-membered intermediate
can occur when 2-3 is used as an enoate, and may also explain why linear side products aren’t
typically seen using β-substituted enoates.55
2.6 Summary and Conclusions
In summary, the mechanism of a three-component coupling reaction (Figure 2-4) was studied.
Prior work from both Montgomery50 and Ogoshi51 has shown that multiple mechanisms are
possible in the reductive [3+2] cycloaddition of an enoate and alkyne, leaving the mechanism of
the three-component coupling reaction developed by Jenkins as ambiguous. In evaluating the
potential energy surface of the three-component coupling, it was found that both an aldol-first
mechanism involving a 7-membered metallacycle, and a ketene-first mechanism involving a
ketene intermediate, are feasible reaction pathways. The ketene-first mechanism (labelled pathway
C) appears to be preferred, due to the ability of ketene elimination to outcompete isomerization to
the 7-membered metallacycle. However, a precarious balance exists between path C and an inner-
sphere aldol-first mechanism (labelled pathway A). Small perturbations in the reaction conditions,
such as using an α-substituted enoate rather than a β-substituted one, appear to be capable of
shifting the mechanism towards aldol-first pathway A. This carries implications for any future
work with nickel-catalyzed reductive [3+2] cycloadditions, including Chapter 3 of this thesis. This
study also showcases the limits of presuming a catalytic mechanism based off of similar prior
work. It is possible for two slightly different substrates to react with the same catalyst to make the
same corresponding product, but to do so through completely different mechanisms.
Experimentalists should use this work as an example for why one should use caution when
applying their untested mechanistic postulations to new reactions.
29
Chapter 3: Elucidation of the Activation Mechanism of Air-Stable
Nickel(0) Catalysts
Some of the material presented in this chapter has been reported in ACS Catalysis.56
3.1 Motivation for the Development of Air-Stable Nickel Pre-Catalysts
Homogeneous nickel catalysis has seen considerable advancements over the past two decades.57–
59 Nickel has played a role in transformations such as C-C bond formation,60–63 C-N bond
formation,64,65 C-O bond formation,65 C-O activation,61,66–68 C-H activation,69–71 decarbonylative
couplings,72 π-component couplings,54,73 and polymerization reactions.74 While related group 10
metal palladium was the dominant catalyst for many of these transformations, resulting in the 2010
Nobel Prize in Chemistry,75 nickel has seen an increase in interest, not only as it is over 5,000
times more abundant in the earth’s crust,76 but also because it is unique suited for reactions such
as alkyl cross-coupling or π-component coupling.57
Despite the great promise of nickel catalysts, there are still many barriers to its adoption. Compared
to palladium, nickel generally requires higher catalyst loadings.77 Additionally, many of the
commonly used nickel precursors, such as Ni(COD)2 (bis(cyclooctadiene)nickel(0)), are air-
sensitive, and require the use of a glovebox.57 Both of these problems can potentially be addressed
through the development of new, air-stable nickel pre-catalysts.
The use of pre-catalyst, with the desired ligands already bound to the metal center, is an effective
strategy for lowering the amount of catalyst needed for a chemical transformation.77 In-situ
complex formation introduces ambiguity about the nature and quantity of active catalyst involved
30
in the reaction. A portion of the metal introduced may fail to ligate, or may be ligated in an
unproductive manner. If only a small portion of the metal and ligand introduced form an active
catalytic complex, then observed catalyst turnover number will be artificially lowered. The failure
of the majority of introduced metal to form a competent catalyst artificially lowers the observed
turnover number. Consequently, by using a pre-catalyst, where all of the material is already ligated,
similar yields to in-situ procedures can be obtained using much lower catalyst loadings, or much
higher yields can be obtained with the same catalyst loading.
Figure 3-1. Use of a pre-catalyst dramatically improves the yield of 3-1. Crystal structure taken from reference 78.
An example of this effect is illustrated by a publication from the Montgomery group.78 A nickel(0)
catalyst in conjunction with small NHC (N-heterocyclic carbene) ligand ITol was found to be an
effective combination for the deoxygenative coupling of an unsaturated aldehyde or ketene with
an alkyne, to form skipped diene species 3-1 (Figure 3-1). While the in-situ formation of the
catalyst gave poor yields, use of pre-ligated complex 3-2 gave much improved yields. The success
of 3-2 as a catalyst in this transformation demonstrates the power of using a pre-catalyst: the same
31
amount of metal and ligand are used, but using an isolable, pre-ligated species ensures that all of
the material added is catalytically active.
Figure 3-2. (Top) Air-stable Ni(II) catalysts require a transmetallation reagent. (Middle) Tradeoffs in the development
of Ni(0) pre-catalysts. (Bottom) Molecular orbital diagram for the π backbonding interaction.
Many of the reactions developed by the Montgomery group have utilized a low-valent nickel
complex in conjunction with an NHC ligand, largely for the purposes of coupling π-components.54
While air-stable pre-catalysts that include a ligated NHC ligand already exist, most of them are
Ni(II) species such as 3-379 and 3-480. Such Ni(II) precursors are competent for reactions that
involve a transmetallating reagent, and do not have a clear means of activation for reactions that
32
only involve π-components and silanes (Figure 3-2, Top). For this reason, Ni(0) pre-catalysts
bound to π-acceptor ligands such as 3-5,81 3-6,82 3-2,78 or 3-783 were considered. In the choice of
olefin, a tradeoff emerges between catalyst activity and air-stability (Figure 3-2, Middle). The
more electron-poor the ligand, the better it is able to engage in a π-backbonding interaction, where
the d orbitals of the metal interact with the π* antibonding orbitals of the olefin (Figure 3-2,
Bottom). A greater the backbonding interaction increases the stability of the complex, as it pulls
electron density away from the metal center, reducing the metal’s susceptibility towards oxidation.
However, an increased backbonding interaction will also increase the π-acceptor’s binding energy,
make fumarate dissociation more difficult, and preventing the generation of an active catalyst.
3.2 Investigating a Diverse Set of Nickel Fumarate Complexes
In this context, the development of an air-stable nickel catalyst with a carbene ligand already bound
was sought. Fumarate complexes such as 3-7 were chosen as a starting point in this investigation,
as such complexes were reported to be air-stable,83 but unreactive towards π-component couplings
in our hands. Given the trends seen with olefin ligands, it was expected that an inverse relationship
between reactivity and stability would occur. With this hypothesis in hand, the design strategy was
to develop fumarate catalysts that might have greater steric clashes with the NHC ligand,
weakening the fumarate-Ni interaction enough to enable ligand exchange (Figure 3-3, Top).
Visiting student Santiago Cañellas and Montgomery student Alex Nett synthesized nine different
fumarate complexes using the IMes NHC, and then they tested their ability to engage in the
reductive coupling reaction to produce 3-9 (Figure 3-3, Bottom). In general, all of the tested
fumarate complexes were found to be more active than Cavell’s originally reported complex (I).83
Most of the aryl fumarate complexes gave low to moderate yields (E, F, G, H), but complexes of
fumarates A and C gave high yields of 3-9, as well as complexes of alkyl fumarates B and D.
33
These 4 fumarate complexes were then subsequently tested for their air stability, and all 4 (A
through D) were found to be air-stable.
Figure 3-3. (Top) Different fumarate complexes were synthesized. (Bottom) The different complexes were tested for
their ability to catalyze a reductive coupling reaction.
However, the discovery of air-stable, reactive Ni(0) IMes fumarate catalysts was not found to be
easily transferred to other NHCs. For instance, Montgomery group student Amie Frank was unable
to use complexes of fumarate A with a chiral NHC,84 or smaller carbene ligand BAC85 for a
reductive coupling reaction, even at higher catalyst loadings compared to complex 3-8-A. The
incompetence of catalysts 3-10-A and 3-11-A suggested that a greater understanding of the catalyst
activation process was necessary, and that the identity of the fumarate used may need to be tuned
based on the NHC used in the complex.
34
Figure 3-4. Other complexes of fumarate A are not competent in reductive couplings.
3.3 Overturning the Original Hypothesis that Catalyst Activation Occurs via Dissociation
Figure 3-5. The mechanism of the reductive coupling reaction. Originally ligand dissociation was believed to be the
means of catalyst activation.
In the synthesis of complexes 3-8, the design strategy was to change the identity of the R group to
increase steric repulsion between the fumarate and metal center. Given the mechanism of the
35
reductive coupling reaction (Figure 3-5), it was thought that the metal center needed to have 2 free
coordination sites in order to perform catalysis. This necessitates some form of ligand dissociation
to allow for binding of the alkyne and aldehyde starting material.
Figure 3-6. The relationship between the free energy of ligand exchange and the yield of 3-9 in reductive coupling
attempts with the corresponding catalyst. Computational details are included in the appendix.
Notably, the hypothesis that dissociative ability of a fumarate complex determines its catalytic
ability can be easily tested computationally. The free energy of ligand exchange was calculated
for each fumarate complex listed in Figure 3-3, and then that energy was compared to the yield of
3-9 that was observed experimentally. If it was the case that ligand dissociation determined
catalytic ability, it would be expected that some form of statistical relationship should emerge
36
between the free energy of dissociation and the observed yields. However, no relationship between
reaction yield and computed binding affinity was found (Figure 3-6).
The lack of correlation seen in Figure 3-6, suggested that a fumarate dissociation mechanism was
not the mechanism of catalyst activation, as was originally thought. As fumarate dissociation for
all of the studied complexes 3-8 was found to be endergonic, it can be concluded that all of the
studied fumarates can act as a catalyst poison. Even if the weakest bound fumarate, D, is
considered, it would be expected that dissociation of 3-8-D to form a nickel-aldehyde-alkyne
complex would raise the energy of the subsequent oxidative addition step by 13.8 kcal/mol,
slowing the reaction down by a factor of over 10 billion. It follows then, that since many members
of catalysts 3-8 are capable of producing 3-9, it must be the case that their corresponding fumarates
are consumed prior to formation of product 3-9. Were this hypothesis to be true, it should be
possible to isolate the products of such a fumarate consumption reaction. Using this prediction,
Montgomery student Ellen Butler investigated the reactivity of catalyst 3-8-A in greater detail.
Under conditions similar to the reductive coupling reaction, products 3-12 and 3-13 were isolated
by reacting 3-8-A with phenyl propyne, 4-fluorobenzaldehyde, and triethyl silane. (Figure 3-7).
As 3-12 is very similar to the products formed in the three-component coupling studied in Chapter
2, we hypothesized that catalyzed activation would occur through an analogous reaction.
Figure 3-7. The isolation of products 3-12 and 3-13 from catalyst 3-8-A.
37
3.4 Investigating the Activation Sequence of BAC and IMes Fumarate Complexes
Figure 3-8. Possible activation mechanisms for complexes of fumarate A.
In Chapter 2, the formation of 3-component products such as 3-12 was found to occur through
either an aldol-first or ketene-first type mechanism, depending on the identity of the π-component
used in the transformation (Figure 3-8). To distinguish between the mechanisms of catalyst
activation in 3-8-A, as well as to investigate why catalyst 3-10-A fails to successfully activate, the
mechanism of catalyst activation of both the BAC and IMes complexes with fumarate A were
investigated computationally.
38
Figure 3-9. The initial steps of activation for IMes complex 3-8-A (blue and turquoise) and BAC complex 3-10-A (red
and pink). Dark colors (red, blue and black) represent aldol-first path A. Light colors (pink, turquoise, and gray)
represent ketene-first path B. Energies are given in kcal/mol, with enthalpies listed in parentheses. Computational
details are included in the appendix.
The potential energy surfaces of the early steps of aldol-first path A and ketene-first path B for
both IMes catalyst 3-8-A (pathways shown in blue and turquoise, labelled as IMes) and BAC
catalyst 3-10-A (pathways shown in red and pink, labelled as BAC) are shown in Figure 3-9. In
Chapter 2, it was demonstrated that the selectivity between an aldol-first reaction and a ketene-
first reaction is dependent on the barrier of ketene elimination compared to the highest barrier step
in the aldol-first process. The early steps listed in Figure 3-9, therefore, play a large role in
determining the path-selectivity of catalyst activation in 3-8-A and 3-10-A.
39
In the initial steps of path A (dark colors), 5 membered metallacycle I rotates to isomer II, and
then isomerizes to ξ-3 bound III-A (TS-II-A). Complex III-A then isomerizes again (TS-III-A)
to 7-membered metallacycle IV-A. Alternatively, in path B (light colors), isomer II extrudes a unit
of aryloxide (TS-II-B), to create ketene complex III-B. The ketene species can then cyclize (TS-
III-B) to carbocyclic species IV-B.
BAC catalyst 3-10-A and IMes catalyst 3-8-A differ significantly in these early steps. For the BAC
complex, ketene elimination (BAC-TS-II-B, 13.4 kcal/mol) is fast enough that it outcompetes
isomerization of ξ-3 bound BAC-III-A to 7-membered metallacycle (BAC-TS-III-A, 19.5
kcal/mol). After forming ketene complex BAC-III-B, an irreversible carbocyclization can occur
(BAC-TS-III-B, 7.1 kcal/mol), yielding carbocycle BAC-IV-B. Taken together, the larger barrier
height of BAC-TS-III-A (19.5 kcal/mol) compared to BAC-TS-II-B (13.4 kcal/mol) indicates
that BAC complex 3-10-A prefers to undergo catalyst activation through path B.
However, IMes catalyst 3-8-A behaves differently. For the IMes catalyst, isomerization of 5-
membered IMes-II-A to ξ-3 bound IMes-III-A is the slowest step towards the formation of 7-
membered IMes-IV-A (IMes-TS-II-A, 15.1 kcal/mol). Unlike the BAC complex, ketene
elimination (IMes-TS-II-B, 22.0 kcal/mol) is too slow to outcompete isomerization to the 7-
membered metallacycle. Due to the higher barrier for ketene formation, and the lower barriers for
isomerization to the 7-membered metallacycle, path A is still a possible activation mechanism for
the IMes catalyst, and would be expected to be the preferred mechanism of activation if it forms
an intermediate that is sufficiently exergonic compared to starting metallacyle IMes-I.
As the preliminary steps for paths A and B suggested that IMes catalyst 3-8-A and BAC catalyst
3-10-A undergo activation by different mechanisms, we hypothesized that the difference in
mechanism can explain why 3-8-A is a competent catalyst, but 3-10-A is not. In order to evaluate
40
this hypothesis, the progress of path A with 3-8-A and path B with 3-10-A was traced further down
their respective potential energy surfaces.
Figure 3-10. Pathway A of the activation of IMes catalyst 3-8-A, part 1. Energies are given in kcal/mol, with
enthalpies listed in parentheses. Computational details are included in the appendix.
In the case of catalyst 3-8-A, path A provides a means to release a potential active catalyst. Figures
3-10 and 3-11 detail the pathway for catalyst release. Seven-membered metallacycle IMes-IV-A
can ligate to an aldehyde (IMes-V-A, Figure 3-10), and can then undergo an aldol reaction (IMes-
TS-V-A) to yield complex IMes-VI-A. Notably, this process has a slightly higher barrier than the
isomerization process (15.9 kcal/mol), but still outcompetes ketene elimination (IMes-TS-II-B,
22.0 kcal/mol, Figure 3-9). After aldol addition, ligation of tetrahydrofuran to complex IMes-VI-
41
A is possible (IMes-VI-A-THF), but an irreversible hydrosilylation (IMes-TS-VI-A) can occur,
yielding complex IMes-VII-A. Complex IMes-VII-A can then rearrange to nickel hydride species
IMes-VIII-A. Subsequently, IMes-VIII-A could either undergo ester reduction (IMes-TS-VIII-
Z, 7.0 kcal/mol, Figure 3-11) to form IMes-IX-Z, or undergo a carbocyclization event (IMes-TS-
VIII-A, -7.8 kcal/mol). The latter process is preferred by a significant margin, and leads to nickel
alkoxide species IMes-IX-A, which can easily extrude an alkoxide to yield compound 3-13 and
an activated catalyst.
Figure 3-11. Pathway A of the activation of IMes catalyst 3-8-A, part 2. Path Z details the possible ester reduction
reaction, and is shown in seafoam green. Energies are given in kcal/mol, with enthalpies listed in parentheses.
Computational details are included in the appendix.
While IMes catalyst 3-8-A has been shown experimentally to be a competent catalyst in the
production of 3-9 (Figure 3-3), the same cannot be said for BAC catalyst 3-10-A (Figure 3-4).
Computational investigation of path B of catalyst 3-10-A reveals a putative reason why that might
42
be the case (Figure 3-12). Cyclization of ketene complex BAC-III-B yields carbocycle BAC-IV-
B (Figure 3-9). Notably, the presence of a proximal ester moiety in BAC-IV-B allows for direct
coordination of the ester to the nickel center (BAC-V-B, Figure 3-12). In effect, by occupying a
coordination site, the proximal ester prevents the coordination of an aldehyde that is reported in
Chapter 2. The stability of BAC-V-B, and the additional chelation that occurs in the complex, can
explain why BAC catalyst 3-10-A is ineffective.
Figure 3-12. (Left) Complex BAC-IV-B can rearrange into carbonyl bound complex BAC-V-B. (Right) A three-
dimensional representation of complex BAC-V-B.
3.5 Preliminary Results Towards the Development of an Air-Stable Nickel(0) BAC Catalyst
The difference in activation mechanism between BAC complex 3-10-A and IMes complex 3-8-A
can explain why 3-8-A is active in reductive coupling reactions, but 3-10-A is not. With a
relationship between catalyst activation mechanism and catalyst efficacy suggested, the next
logical step is to develop a catalyst that goes through an “aldol-first” mechanism, so as to avoid
catalyst trapping by developing a species such as BAC-V-B (Figure 3-12). As the fate of catalyst
3-10-A is determined in part by the barrier of ketene elimination (BAC-TS-II-B, Figure 3-9)
compared to isomerization (BAC-TS-III-A, Figure 3-9), the transition states for ketene
43
elimination and metallacycle isomerization were evaluated for a variety of different BAC fumarate
complexes (Figure 3-13). Of the 12 fumarates tested, only 3 (B, I, J) were found to favor
metallacycle isomerization over ketene elimination. Additionally, 3 more fumarates (C, K, M) had
metallacycle isomerization within 1 kcal/mol of ketene elimination. In all 6 cases, the difference
in energy between the two possible isomerization mechanisms is within the reported error for the
functional used in the analysis, ωB97X.13 For this reason, the 6 fumarates listed (B, C, I, J, K, M)
are viable candidates for experimental study.
Figure 3-13. Preliminary efforts towards developing a BAC fumarate catalyst. Fumarates that favor metallacycle
isomerization over ketene elimination are shown in blue. Fumarates where metallacycle isomerization is within 1
kcal/mol or less than ketene elimination are shown in purple. Listed energies are free energies in kcal/mol, and are
relative to BAC-I (Figure 3-9). Computational details are included in the appendix.
The fumarate R groups where metallacycle isomerization is competitive with ketene elimination
have a diverse steric and electronic profile, ranging from small substrates (I, J) to bulky substrates
(K, M), and including both aryl (C, M) and alkyl (B, I, J, K) groups. A clearer pattern exists for
the fumarates that clearly favor ketene elimination (D, E, F, G, H, L). Almost all of these fumarate
44
R groups are aryl species, and are generally non-bulk aryl groups. For instance, in all of the tested
aryl substrates that lacked an ortho substituent (E, G, H), ketene elimination is favored over
metallacycle isomerization by at least 6 kcal/mol.
Additionally, the competitiveness of metallacycle formation appears to be driven more by
destabilizing the ketene elimination step, rather than stabilizing the isomerization process. The
lowest barrier ketene elimination step (10.6 kcal/mol, F) is much lower in energy than the lowest
barrier isomerization step (17.8 kcal/mol, M). This presents a problem in catalyst development, as
if metallacycle isomerization needs to be fast enough to enable catalyst release. Interestingly, all
of the aryl fumarates tested have lower barriers for metallacycle isomerization than any of the alkyl
fumarates tested.
While the data presented here represent only a preliminary study into the factors that affect
selectivity for path A over path B, some key insights into the factors that affect path selectivity can
be gleaned. Alkyl groups appear to generally favor isomerization over elimination, but the barriers
for both processes appear to be higher compared to aryl groups. Aryl groups, in turn, appear to
generally favor elimination over isomerization, but both processes are lower in energy. Steric bulk
also appears to have a positive effect in making the isomerization process more competitive than
elimination, which is consistent with what was observed in Chapter 2 with α-substituted enoates.
Taken together, the most promising fumarate tested in Figure 3-13 appears to be fumarate M. This
fumarate has the lowest barrier for metallacycle isomerization among the tested set, and while
ketene elimination is favored, it is only favored by an amount within the error of the calculation
(0.6 kcal/mol). Future developments in creating a bulkier version of M may allow for the
development of an air-stable Ni(0) BAC complex.
45
3.6 Summary, Conclusions, and Outlook
In summary, the mechanism of activation of nickel NHC fumarate complexes has been identified.
The original hypothesis of ligand displacement was disproven by comparing the binding energies
of the fumarate to the yield of product observed experimentally. Based on these initial
computational results, a new hypothesis of fumarate consumption during catalyst activation was
crafted, ultimately leading to the experimentalists identifying products of the associated fumarate
consumption reaction. The isolation of fumarate consumption species 3-12 and 3-13 determined
that catalyst activation occurs through a reaction analogous to the three-component coupling
reaction detailed in Chapter 2. Using the three-component coupling as a guide, catalyst activation
through both an aldol-first and ketene-first pathway was examined computationally. It was found
that active IMes catalyst 3-8-A undergoes an aldol-first catalyst activation mechanism, but inactive
BAC catalyst 3-10-A undergoes a ketene-first activation mechanism, where it becomes trapped as
ester-bound complex BAC-V-B. Preliminary work has been done to find a fumarate that can be
paired with BAC that would ensure that the BAC catalyst is activated through an aldol-first
mechanism, and avoid catalyst trapping.
46
Chapter 4: Synergistic Effects Between Radical Attack and Applied
Force in the Depolymerization of Poly(Acrylic Acid)
4.1 The Potential Energy Surface Under Applied Force
Chemists have used tools such as photoexcitation, applied electric potentials, or simply the
manipulation of temperature to alter the kinetics and thermodynamics of chemical reactions. The
application of an external mechanical force represents another avenue to introduce energy into a
chemical system.86 Through the introduction of a force bias, chemical reactions that are
endergonic, or are too high in barrier to proceed at a reasonable rate, become accessible to
chemists.
Figure 4-1. The additive effect of applied force on the Morse potential. The distortion due to applied force is greater
at larger C-C bond distances.
Bond scission events are a classic example of how an applied mechanical force can change the
nature of chemical reaction. A carbon-carbon (C-C) bond has a homolytic bond dissociation
energy of approximately 90 kcal/mol,87 and due to this high endothermicity, C-C bond scission is
47
not expected to occur spontaneously. However, if an external force is applied, the energy of a
chemical system decreases as the two carbons move further and further apart. This means that
eventually, at a large enough distance, C-C bond scission becomes exothermic, and
thermodynamically favorable. Figure 4-1 details the effect that applied force has on a potential
energy surface. If we consider the C-C bond as adopting a Morse potential (A), we can then
combine that potential with an external force (B) to create a force-modified potential (C). In
potential C, bond scission is exothermic, but there a barrier associated with the bond scission event,
that is dependent on the amount of force required.
Figure 4-2. Estimating the tensile of a C-C bond using the Morse method.
Considering a chemical bond as a Morse oscillator has the additional advantage of allowing for an
estimation of the tensile strength of the bond (FT, the force required to break the bond). The first
derivative of the Morse potential is the force that the potential exerts on the chemical bond (internal
48
force). Applying an external force, then, can be seen as counteracting the internal forces of the
bond. If it is assumed that a bond breaks when the no barrier for scission exists, it can then be
inferred that the tensile strength of a bond is simply the maximum of the first derivative of the
Morse potential. Using the functional form of the Morse potential, the tensile strength can be
derived, yielding a dependence only on the bond dissociation energy (E0 ), and bond force constant
(𝑘) (Figure 4-2).88
Figure 4-3. The expected effects of force according to the tilted potential energy surface model.
Of course, in reality, bond scission events can occur even if a kinetic barrier exists. Preliminary
work by Zhurkov has shown that applied force has a linear effect on such a kinetic barrier, enabling
a low barrier for reaction (and thus faster rate of reaction) with an increase in applied force.89 Force
is also expected to change the geometries of the intermediates involved. This is adequately
described by the tilted potential energy surface model (TPES) (Figure 4-3). In general, with
increasing external force, it is expected that the starting geometry (Start) of the material becomes
more product-like with increasing force, and the transition state (TS) becomes more reactant-like.
49
The net effect of this process is that the starting structure and the transition state become more
similar with increasing applied force.
Computational methods offer an avenue to investigate mechanochemical processes.90,91 A
common method of computational investigation is the COGEF (constrained geometries simulate
external force) method. In COGEF, the potential energy surface of stretching a molecule is mapped
using a series of geometry optimizations with an increasing distance constraint. In the seminal
paper of the method, Beyer uses the information derived from this potential map to estimate the
tensile strengths of various bonds, including C-C, C-N, and Si-O at various timescales.92 Notably,
the method cannot identify the transition state of the bond scission event, as it infers activation
energies from a theoretical force-modified potential that is based off of the curvature of the
potential energy surface under no force (similar to the Morse model described in Figure 4-2).
Despite this limitation, COGEF still finds use in exploring mechanochemical processes; for
instance, in comparing the COGEF potential of unprotonated vs protonated dimethyl ether, Beyer
finds that proton affinity of an ether increases with applied force,93 supporting a previous Carr-
Parinello dynamics study that demonstrated the role of aqueous solvation in the depolymerization
of poly(ethylene glycol).94 In complicated systems such as lignin, ab initio steered molecular
dynamics (AISMD) have been used to identify the bonds most susceptible to scission during
depolymerization.90 AISMD has also been used to identify the heterolytic character of poly(o-
phthalaldehyde) depolymerization.95
While popular tools such as COGEF are unable to provide a transition-state geometry,92 recent
developments in the growing string method allow for the identification of transition states in the
presence of an applied force (F-GSM).96 In this chapter, F-GSM is the method of choice for
interrogating bond scission events, allowing for detailed analysis on the transition state geometries
50
of the processes. The tool works in a similar fashion to GSM (see Section 1.5), with the addition
that the energy of a given state is modified by the term −𝐹 ∗ ∆𝑥, where 𝐹 is the applied force, and
∆𝑥 is the change in distance between the atoms upon which force is applied.
4.2 Plastic Recycling Using Ultrasonic Depolymerization
Plastic waste accumulation in the environment occurs on a massive scale, where it is predicted that
the mass of plastics in the ocean will exceed the total biomass of fish by the year 2050.97 This
problem might be somewhat alleviated by recycling, but the United States only recycles roughly
9.1% of plastic waste, a low figure compared to recycling rates for paper (66.6%), glass (26.4%),
and metals (34.3%).98 The recycling rate of plastics is limited99 by methods that mechanically
repurpose certain plastics for new applications, usually resulting in lower quality materials which
reduces economic incentives to recycle. For this reason, chemical methods of recycling such as
depolymerization attract interest due to their potential to reach a greater scope of materials and
create more valuable recycled products. By developing and expanding recycling technologies such
as depolymerization, the recycling rate for plastics could be greatly improved, ultimately having a
great positive impact on the environment.
A promising depolymerization strategy is to use the mechanochemical technique of ultrasonic
irradiation. (Figure 4-4, A).100 In ultrasonic depolymerization, an acoustic field with frequencies
of greater than ~20 kHz is applied to a solution of polymer.88,91,101–105 The pressure variations
imparted by the high frequency sound waves form cavitation bubbles in solution that ultimately
collapse (Figure 4-4, B), producing a shear force that is capable of tearing polymer chains apart
(Figure 4-4, C). Additionally, pyrolytic reactions in the cavitation bubbles are known to produce
free radicals (Figure 4-4, D). These radicals are believed to accelerate the process of polymer
51
degradation,106 as introduction of an external radical source has been shown to increase the
breakdown rate.107–114
Figure 4-4. Recycling of polymers is enabled by ultrasonic depolymerization.
Prior studies have considered the roles of mechanical force and radical species—each separately—
in the process of ultrasonic irradiation. Based on studies with degassed solvent,115 and the observed
propensity for midpoint scission to occur,116 the mechanical forces generated though cavitation
bubble collapse are thought to be the dominant source of bond scission.88,90,101 Mechanical scission
generally occurs through a homolytic pathway,88,101,102 resulting in the formation of two free
macroradicals. These homolytic cleavage events have been observed by monitoring the
52
stoichiometric consumption of a radical trap.117 Macroradicals have also been directly observed
through EPR studies during the sonication process.118
As a consequence of the depolymerization mechanism largely being mechanical scission,
depolymerization is expected to occur until the molecular weight of the polymer converges to a
limiting value. The origin of this effect is best explained by a model developed by Okkuama and
Hirose.119 In their model, the force that a polymer experiences is due to the friction of the monomer
units with the surrounding solvent. Consequently, the overall force that a given polymer strand
feels is proportional to the number of monomers in a given strand. While the force experienced by
each polymer strand shrinks as the strand gets shorter, the tensile strength of the polymer remains
constant. The limiting length of a given polymer, then, is simply the length at which the forces
experienced by the polymer strand are insufficient to cause further chain scission. Simon has used
this model to accurately simulate the time evolution of polymer degradation.120
Separate from the formation of polymer macroradicals during ultrasonic polymerization, small
radical species are also known to form during the cavitation process.121 As cavitation bubbles
grow, the frequency of their vibration increases, heating the interior of the bubble to several
thousand degrees Kelvin. At such high temperatures, volatile compounds in the bubble, such as
solvent molecules, can pyrolytically disproportionate to small radicals. These radicals are known
to escape from the cavitation bubble and enter solution, where they can react with dissolved
materials.122–125 The free radicals that are generated are also known to initiate radical
polymerization in solutions of monomer.126
Quenching studies have shown that free radicals can play a role in the depolymerization process
as well. Koda106 has shown that the addition of radical scavenger tert-butanol inhibits the ultrasonic
degradation of various polymers. Likewise, the introduction of radical-generating species is known
53
to accelerate ultrasonic degradation processes. The Chen group, as well as others, have reported
depolymerization processes that combine Fenton chemistry with ultrasound.107–111 Yao has
reported a synergistic effect of bubbling ozone during the ultrasonic irradiation of chitosan
solutions.113 Gogate has shown that addition of oxidant potassium persulfate is beneficial in the
degradation of guar gum using hydrodynamic cavitation.112 This group also found that addition of
H2O2 or ozone aids in the ultrasonic depolymerization of poly(acrylic acid).114
The interplay between radical and ultrasonic degradation plays an important role in breaking down
polymers, but the specific mechanism(s) involved in this synergy is not fully explicated. Koda,106
for instance, proposes random chain scission events as an explanation for why free radicals affect
ultrasonic polymer degradation. In Koda’s report, however, it was also observed that the limiting
molecular weights of the degraded polymers change in the presence or absence of a radical
scavenger. The implication of this observation is that in the presence of radicals, there is a change
in how the polymer responds to mechanical force, as the limiting length effect is due exclusively
to mechanochemical degradation. Based on this implication, it appears that the radical species
formed during ultrasonic degradation play a role beyond that of enabling simple random chain
scission events.
Figure 4-5. This chapter explores the synergistic interplay between radical attack and tensile force.
This chapter seeks to provide a clear, atomistic picture of how radical species affect the
sonochemical depolymerization process (Figure 4-5). The synergistic effect of radical attack and
54
tensile force in the ultrasonic depolymerization of poly(acrylic acid) (PAA) will be described. PAA
was chosen as it is broadly used as a super-absorbent polymer, as well as in paints, dentistry, and
other applications.114 The origin of the change in limiting length observed during depolymerization
can be explained though the interplay of radical attack and application of mechanical force. Radical
attack will be shown to have a weakening effect on the tensile strength of the polymer, which will
affect the limiting length. The effects of force on the transition state energy of bond scission will
be quantified, allowing for the inclusion of thermal effects. Finally, it will be shown that radical
attack causes the polymer to respond to force in a manner distinct from what is normally seen in
mechanochemistry.
4.3 Evaluating the Impact of the Weak Bond Effect Using a Morse Potential
Incorporation of a weak bond into a polymer backbone is expected to accelerate the rate of chain
scission.91 For example, when Encina and coworkers added peroxide linkages in
poly(vinylpyrrolidone), the rate of ultrasonic degradation increased by a factor of 10.127 Using
diazo-linked polymers, Moore and coworkers provided evidence that cleavage is mostly localized
at weak bonds.128 This “weak bond effect” suggests that radical activation of PAA might synergize
with tensile force to break down this polymer. While the homolytic bond dissociation energy of a
carbon-carbon bond is generally in the vicinity of 90 kcal/mol,87 the heat of (radical)
polymerization for polyolefins is much lower, in the range of 10-30 kcal/mol.129 Acrylate
polymerizations are in the vicinity of 19 kcal/mol,129 suggesting that lower forces will break the
weakened C-C bond in activated PAA.
55
Figure 4-6. Model systems used in this study: Degradation of PAA through force alone (PATH-1), and force in
conjunction with radical attack (PATH-2).
Two model systems of PAA were used to quantify the bond-weakening effect of radicals (Figure
4-6). The first is a tetramer of AA with inactivated C-C bonds (1), which can be fragmented via
tensile force into a biradical (3+4). This degradation pathway is called PATH-1. The second (2)
is similar to 1, except one hydrogen atom from the backbone has been removed, for example by
radical abstraction via a sonication-generated hydroxyl. C-C bond breaking for the radical-
activated species is denoted PATH-2.
Figure 4-7. Flowchart for evaluating tensile strength using the Morse method. The complete procedure is described
in the appendix.
These pathways were first examined by treating the polymer scission as a purely mechanical event
using the Morse method. A flowchart detailing this process is shown in Figure 4-7. A library of
conformations of 1 and 2 were first generated. Conformers of 1 were generated using the Confab
56
tool130 in Open Babel,131 which resulted in 8 unique conformers. Conformers for 2 were generated
by abstracting an α-hydrogen from each of the conformers of 1. As hydrogen bonding is known to
affect the heat of polymerization of protic polymers such as PAA,132 and to ensure that the
conformers used in this study are consistent with aqueous solvation, explicit water solvation was
modeled. For each conformer of 1 and 2, the system was surrounded by a 6 Å water shell
containing 260 water molecules. Molecular dynamics (MD) simulations were then used to create
a series of snapshots of the tetramer in an aqueous environment.
Figure 4-8. Example three-dimensional representations of the tetramer (Right) and dimer+dimer (Left) systems used
for this study. These represent two of many snapshots used for this study.
The geometry of selected snapshots was then re-optimized using a non-periodic quantum
mechanical/molecular mechanical (QM/MM) method. After optimizing the geometry of the
snapshots (Figure 4-8, Left) the scissile bond (shown in red, Figure 4-7) was cleaved by applying
a stretching force of 10 nN between the two atoms of the scissile bond using the EFEI (external
force explicitly included) method.133 After bond scission, subsequent re-optimization yielded two
57
PAA dimers (referred to as dimer+dimer snapshots, seen in Figure 4-8, Right). A complete
description of the entire procedure can be found in the appendix.
As denoted in Figure 4-2, the tensile strength of a bond can be determined from its bond
dissociation energy (E0 ) and the bond’s force constant (k ). The bond dissociation energy was
determined by comparing the total energy of each dimer+dimer snapshot to the tetramer from
which it came. By averaging the difference in energy for each set of snapshots, a value for the
enthalpy of bond scission is obtained. To determine the force constant of the scissile bond, a
vibrational constant was determined from each optimized tetramer absent any explicit water using
partial hessian vibrational analysis.134 The calculated force constant values were averaged to yield
the force constant of the scissile bond.
Figure 4-9. The effect of hydrogen atom abstraction on the tensile strength poly(acrylic acid). Computational details
are included in the appendix.
These values were used in the final equation for tensile strength (FT ) (Figure 4-2). The tensile
strengths of 1 and 2 were calculated as 6.6 nN and 2.6 nN, respectively (Figure 4-9), both within
the range of forces available for sonication.88 Hydrogen atom abstraction, therefore, is calculated
58
to reduce the tensile strength of PAA by approximately 4 nN. As the limiting length of polymer
during sonication is proportional to the square root of the polymer’s tensile strength,119 the results
in Figure 4-9 predict that the limiting length of a polymer weakened by radicals should be ~37%
lower than a polymer free of radical defects. These results are on the order of the changes in
limiting length observed by Koda upon suppression of radical formation during the sonication of
poly(ethylene oxide) and polysaccharides.106
The predicted tensile strength of 1 of 6.6 nN using the simple Morse method is outside the range
of modern estimates of C-C bond strength, such as the thermally activation barrier to scission (5-
6 nN),135 or COGEF (4.5-5 nN) models. This discrepancy likely stems from the assumption that
scission only occurs in the absence of a thermal barrier.92 In reality, it is expected that bond scission
would occur once a thermally accessible barrier is attained. Analysis of the bond scission reaction
using F-GSM will identify the nature of this barrier, and allow for a more accurate determination
of the effect of radical abstraction on the transition state of bond scission and tensile strength.
4.4 Determining the Effect of Radical Abstraction on the Transition State of Bond Scission
Polymer degradation by sonication is better described by treating cleavage events as a chemical
reaction. Using this model, the reactant and transition state geometries—as well as the activation
barrier—depend on the amount of force applied to the polymer chain. Using the sets of tetramers
from the previous section, the transition states of bond scission for PATH-1 and PATH-2 were
found using the force-biased growing string method (F-GSM, see appendix for the full process)
59
for a range of applied tensile forces.96 The activation enthalpies as a function of force from F-GSM
are given in Figure 4-10.
Figure 4-10. The relationship between enthalpy of activation and applied force on the polymer chain. Computational
details are included in the appendix.
Given that hydrogen atom abstraction by a hydroxyl radical is fast (ΔH‡ of ~3 kcal/mol) and
irreversible,136 the selectivity between PATH-1 and PATH-2 is expected to be largely determined
by the availability of hydroxyl radicals in solution. However, the rate of bond scission for PATH-
1 and PATH-2 will still be relevant if hydrogen atom abstraction occurs, as the relative rate
between PATH-1 and PATH-2 will determine whether scission will occur at the point of hydrogen
atom abstraction. Essentially, hydrogen atom abstraction can only possibly be beneficial if it
provides a lower barrier pathway for bond scission to occur.
At low levels of applied force, it is expected that the barrier for bond scission in PATH-1 would
be insurmountably high. For this reason, only the activation energies for forces in the range of 3
to 5 nN are shown for PATH-1. A negative linear relationship between the enthalpy of TS-1 (ΔH‡)
60
is observed (R2 = 0.96), consistent with the Bell model of force-activated chemistry.102 Similarly
to TS-1, the activation enthalpies of TS-2 decrease linearly with applied force (R2 = 0.99), but
slope of only about one-half that of TS-1. Based on this difference in slopes, we can extrapolate
that at forces greater than 6.45 nN, bond scission is expected occur via PATH-1 over PATH-2.
4.5 Determining the Effective Tensile Strength of PAA With and Without Radical Attack
In bulk materials, the tensile strength of a material is defined as the maximum tension that a
material can withstand before breaking. However, in looking at a single polymer strand, and
considering the thermochemistry of bond scission, bond scission becomes inevitable as long as it
is exergonic. A more informative measure of mechanical strength in bonds is describing the half-
life of the scission process at a given force and temperature. Thus, we define the effective tensile
strength (E)FT, as the amount of force needed to lower the half-life to small enough time that bond
scission would be expected to occur. Notably, (E)FT is a context-dependent quantity. For instance,
applications that occur at longer timescales would need a lower force for bond scission to occur,
as longer half-lives could be useful for that application.
For the purposes of this work, we are most concerned with timescales and temperatures that are
relevant during ultrasonic depolymerization. Bubble collapse has been previously modeled as
occurring within a 1 μs timescale.137 While acoustic bubbles are known to form local hot spots,138
we will focus on the temperature of the bulk solution, and assume a room-temperature reaction.
Local hot-spots are known to reach up to 2,000K, and it would be expected that both 1 and 2 would
break apart instantaneously under those conditions. Additionally, while the enthalpy of
polymerization of PAA is known to be 18.5 kcal/mol,139 the ceiling temperature of polymerization
has not been directly measured. However, based on high-pressure polymerizations of acrylic acid,
it is estimated that the ceiling temperature is somewhere around 200°C.140
61
Figure 4-11. Derivation of a relationship between enthalpy of activation (ΔH‡) and reaction half-life (t1/2). Where: kb
is Boltzmann’s constant, T is the reaction temperature, h is Planck’s constant, R is the gas constant, ΔH‡ and Δ ‡ are
the enthalpy and entropy of activation, ΔHpolym and Δ polym are the enthalpy and entropy of polymerization, and Tc is
the ceiling temperature of polymerization.
Entry 𝑡1/2
in μs 𝑇 in
°C 𝑇𝑐 in
°C ∆𝐻‡ in
kcal/mol (𝐸)𝐹𝑇 of
1 in nN
(𝐸)𝐹𝑇 of 2 in
nN
𝐿𝐿1𝐿𝐿2
1 1 25 200 21.1 4.7 2.5 1.37
2 0.1 25 200 19.8 4.9 2.9 1.30
3 1 100 200 26.6 4.1 1.1 1.93
4 1 25 300 19.1 4.9 3.0 1.28
5 0.1 100 200 24.9 4.3 1.6 1.63 Table 4-1.The effective tensile strength of 1 and 2 calculated under different assumptions.
Using these 3 assumptions, in conjunction with an equation relating ΔH‡ to a given half-life
(derived in Figure 4-11) and the relationship between force and TS energy in Figure 4-10, the
effective tensile strength of 1 and 2 can be estimated (Table 4-1, entry 1). How the calculated
tensile strength is expected to change by changing these assumptions is shown in entries 2-5. In
general, the estimated values of (E)FT are lower than those predicted by the Morse model. Changes
in the timescale assumption have a logarithmic effect (Entry 2), but changes in temperature have
62
a dramatic effect on the tensile strength of the material (Entries 3, 5). Changes in the assumption
of the ceiling temperature of PAA appear to have a relatively small effect (Entry 4).
Figure 4-12. A contour plot of the effective tensile strength (E)FT of 1 and 2 assuming a Tc value of 200 °C.
Based off of the relationship between tensile strength and limiting length derived by Okkuama and
Hirose,119 the expected ratio of limiting lengths should be equivalent to the square root of their
ratio of tensile strengths. Using the assumptions in Table 4-1, entry 1), it is estimated that
sonication of PAA in the absence of radicals (PATH-1) should result in a limiting length (LL) that
is 1.37 times the length of what would be expected to be observed in the presence of radicals
(PATH-2). This ratio is affected by the assumptions made, and the details on how the ratio of
limiting lengths can change is also shown in Table 4-1.
A contour plot of effective tensile strength at various temperatures and timescales is shown in
Figure 8. This plot allows for extrapolation of the effective tensile strength of 1 and 2 at
temperatures and timescales beyond the assumptions made in Table 4-1. The effective tensile
strength of 2 is expected to weaken to 0 nN at about 200 °C on a reaction timescale of 0.1 μs, and
at temperatures higher than 400 °C, is expected to have no appreciable tensile strength on a
63
timescale of 10 ps. This is in contrast with 1, which still requires some amount of force for scission
to occur within 10 μs at all temperatures calculated.
4.6 Geometric Distortions Due to Applied Force on the Reactant and Transition State
Figure 4-13. Comparison of key geometries, which suggest that PATH-1 initial and TS structures converge towards
one another as forces increase, but PATH-2 structures do not. Explicit water molecules are removed for clarity.
The large difference in activation energy slope between PATH-1 and PATH-2 is surprising, given
that the two reactions occur with similar polymer backbones (Figure 4-10). This phenomenon
might be explained by the geometric distortions imposed upon the reactant and transition states for
the two pathways. Figure 4-13 details the change in geometry from starting structure to transition
state for selected snapshots at 3 and 5 nN of applied force. From examination of PATH-1, it is
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clear that TS-1 becomes more similar to 1 at 5 nN, compared to at 3 nN (Figure 4-13, A and B).
In particular, this is driven by the fact that at 5 nN, the scissile bond distance of TS-1 is shorter,
and the end-to-end bond length of 1 is longer. This represents a stark difference to the changes in
PATH-2 from 3 nN to 5 nN. Comparing 2 with TS-2 at 3 and 5 nN (Figure 4-13, C and D), the
two structures track each other closely as the applied force changes, due elongation of the reactant
and TS (transition state) at about the same rate.
Figure 4-14. The effects of applied force on the end-to-end lengths in PATH-1 and PATH-2.
Quantitatively tracking the average end-to-end and scissile bond distances in PATH-1 and PATH-
2 confirm the trends seen upon visual inspection of the structures. In the case of PATH-1, with
increasing applied force, the ends of the polymer increasingly elongate (Compound 1, Figure 4-14,
A). However, the end-to-end distance of transition state TS-1 remains relatively stationary,
65
increasing by ~0.1 Å (~1% of length) as the applied force increases (Compound TS-1, Figure 4-14,
A). In essence, at higher force loadings, the end-to-end bond distance of 1 converges to that of TS-
1. The starting and transition state structures of PATH-2 do not exhibit this trend. Rather, both
starting structure 2 and transition state structure TS-2 elongate at a similar rate with increasing
applied force (Figure 4-14, B). At comparable forces, the end-to-end bond lengths of 2 are longer
than 1, while the end-to-end bond lengths of TS-2 eventually converge to similar lengths of TS-1
at ~4 nN.
A better representation of the divergence of the end-to-end bond lengths is to observe how it
changes between the starting structure and transition state at different force values (Figure 4-14,
C). With increasing applied force, the end-to-end distance in PATH-1 decreases at a rate of 0.27
Å per nN of applied force. However, while the end-to-end lengths of 2 and TS-2 consistently
increase with force, in PATH-2 the end-to-end distance only increases at a rate of 0.02 Å per nN
of applied force, essentially keeping the change in polymer length constant between 2 and TS-2.
While in PATH-1 the end-to-end length of 1 converges to that of TS-1 with increasing force, we
see the opposite trend in the change in scissile bond length (Figure 4-15, A). The length of the
scissile bond remains relatively unchanged in 1 with increasing force, but decreases substantially
with increasing force with TS-1. In PATH-2, the scissile bond length in TS-2 decreases at a slower
pace compared to TS-1, while the bond length in 2 is essentially unchanging (Figure 4-15, B). In
both cases, we can interpret this as the transition state of bond scission coming earlier and earlier
in the bond scission event, which is consistent with the notion that under force, the structure of
transition state converging towards starting structure.
66
Figure 4-15. The effects of applied force on the scissile bond distances in PATH-1 and PATH-2.
It is noteworthy, however, that if we look at the change in scissile bond length between the
transition state and starting structure at different force values (Figure 4-15, C), the change in
scissile bond length decreases at a much faster rate in PATH-1 than PATH-2. Just as is seen in
the change in end-to-end lengths (Figure 4-15, C), the geometries of structures in PATH-1 appear
to converge together at higher force values, while in PATH-2, the geometric differences between
TS-2 and 2 are mostly maintained, even at high levels of force.
Under the assumption that the transition state does not appreciably change with increasing amount
of applied force, the change in activation barrier with force for a given reaction is thought to be
caused by the energy of applied force (∆𝑬𝑨𝑭, Figure 4-16), which is simply the energetic
67
contribution stemming from the gradient that force creates.133 In the transition state searching,
force was applied directly to the ends of the polymer, so we measure Δx as the difference in end-
to-end distance between the starting structure and the transition state. Figure 4-16 details the
calculated Δ AF for PATH-1 and PATH-2. In PATH-2, we see a linear relationship between
applied force and Δ AF, with a slope of approximately -5.15 kcal/mol per nN. This approximately
mimics the decrease of 3.97 kcal/mol per nN we see in ΔH‡ with increasing force (Figure 4-10).
However, in the case of PATH-1, Δ AF increases with force, at a rate of about 2.89 kcal/mol per
nN. The ability of ∆𝐸𝐴𝐹 to predict the change in activation energy in PATH-2, and inability to
provide the same prediction in PATH-1, suggests that the application of external force does not
heavily distort TS-2, but dramatically distorts TS-1. This observation is consistent with what is
quantified in Figure 4-14 and Figure 4-15.
Figure 4-16. The energetic contribution from applied force (ΔEAF) observed in PATH-1 and PATH-2. The decrease
in ΔH‡ with force in PATH-2 can be explained though the steady increase in ΔEAF.
According to the TPES model, under application of force, the reactant and TS structures are
expected to become more geometrically similar.86,141 Plots A and B in Figure 4-17 detail the
68
normalized change in scissile bond distance and end-to-end length with force. In both PATH-1
and PATH-2, the scissile bond length of the transition state approaches the scissile bond of the
initial structure. However, in PATH-1, this trend is much more pronounced, and we also see a
similar trend in the end-to-end lengths. The geometric distortion due to force in PATH-1 is so
great that the scissile bond lengths and end-to-end distances appear to be quickly converging to a
single point.
Figure 4-17. Comparing the (relative) end-to-end and scissile bond distances of the starting and TS structures in
PATH-1 and PATH-2. The average end-to-end and scissile bond distances were calculated within each reaction path.
4.7 Rationalizing why PATH-1 is More Responsive to Force Than PATH-2
With the application of force, PATH-1 changes much more rapidly than PATH-2, both in terms
of transition state energy, as well as starting and transition state geometry. As “force
responsiveness” is a consequence of the inverse of the 2nd derivative of the PES,142 the large
differences in response to applied force suggest that the energy profiles of bond dissociation in
PATH-1 and PATH-2 have very different curvatures. Indeed, without radical abstraction, bond
scission in PATH-1 follows a dissociative pathway that does not contain a transition state (Figure
4-18). However, upon abstraction of a radical, bond scission in PATH-2 now follows a pathway
with a transition state (Figure 4-18). A simple analytical model of the two reaction pathways can
69
explain this large difference in force responsiveness. PATH-1 is modeled as a Morse potential,
and PATH-2, as a quartic potential. The choice of these functions reflects the presence or absence
of a transition state that is expected at no force. Each potential energy surface is then modified by
a linear force times distance term, representing the shift of the potential profile with tensile forces.
Parametrization of these energy surfaces was performed to fit the zero-force profiles from
atomistic simulations, see the appendix for more details.
Figure 4-18. Differences in the PES curvature of PATH-1 and PATH-2.
The results of the analytical model are shown in Figure 4-19. The bottom right of Figure 4-19
demonstrates that applying tensile forces has a greater effect on the Morse potential than the quartic
potential. To understand this, the top of Figure 4-19 shows that TS-1 is dragged downward by the
applied force, while TS-2 stays roughly constant. At the same time, 1 and 2 increase in energy at
about the same rate with applied force. The net effect is that applied force reduces the barriers for
TS-1 as well as TS-2, but TS-2’s activation barriers move faster. The relative slope (𝐸𝑆𝑙𝑜𝑝𝑒1
𝐸𝑆𝑙𝑜𝑝𝑒2) of
70
2.1 for this highly simplified model is similar to that of the full atomistic model, with a slope of
2.0.
Figure 4-19. (Top) How the Morse and quartic potentials behave under applied force (Bottom Left) Comparing the
predicted TS energies of PATH-1 and PATH-2 using the example Morse and quartic functions. The ratio of the
change in energy with force (ESlope1 vs ESlope2) is very close to the atomistic model. (Bottom Right) Comparing the
displacement of the location of the TS using the example Morse and quartic functions. The ratio of the change in
displacement with force at the last five data points (DispSlope1 vs DispSlope2) is consistent with the atomistic model.
The simplified model results are also geometrically consistent with the full atomistic model (Figure
4-19, Bottom Left). As the amount of applied force increases, the scissile bond length of TS-1 and
TS-2 move closer and closer to the lengths of respective reactant states 1 and 2. Just as is seen in
the atomistic model, TS-1 changes at a much faster rate compared to TS-2. If we take the slope of
the last 5 datapoints of the TS displacement/force relationship for both TS-1 and TS-2 (𝐷𝑖𝑠𝑝𝑆𝑙𝑜𝑝𝑒1
𝐷𝑖𝑠𝑝𝑆𝑙𝑜𝑝𝑒2),
71
we find that TS-1 is displaced at 3.9 times the rate as TS-2, comparable to the 8-fold difference
that we see in the atomistic model (Figure 4-15, raw numbers are included in the appendix).
4.8 Conclusions
In summary, abstraction of a radical from the polymer backbone is predicted to reduce the tensile
strength of the polymer. Abstraction of a radical decreases the enthalpy of scission from 92.7
kcal/mol to 14.2 kcal/mol. Crudely, we can estimate that this 78.5 kcal/mol decrease lowers the
tensile strength of the polymer from 6.6 nN to 2.6 nN. More accurately, by determining the
transition state of bond scission of 1 and 2, we can derive a linear relationship between applied
force and enthalpy of activation. Using this relationship, we can refine our estimations of the
effective tensile force of 1 and 2 to 4.7 nN and 2.5 nN, respectively, depending on assumptions
about the timescale of bubble collapse, reaction temperature during bond scission, and ceiling
temperature of PAA.
Compounds 1 and 2 are observed to behave quite differently under force. During degradation
through PATH-1, the relative geometries of TS-1 and 1 are significantly perturbed, but in PATH-
2, the corresponding states do not change significantly. This has been measured by observing
marked changes in 1 and TS-1, juxtaposed against the fairly minor changes seen in 2 and TS-2.
By comparing the normalized rate of change of the scissile bond and end-to-end distances to the
normalized change in TS energy in PATH-1, we can assert that the decrease in TS energy is due
to the 1 and TS-1 becoming more geometrically similar with greater force. As the relative
geometries of TS-2 and 2 don’t change nearly as much, we find that ΔEAF provides a good
explanation for the decrease in TS energy seen in PATH-2. The difference in behavior between
the two pathways can be explained as a consequence of the differences in the curvature of the PES
of PATH-1 and PATH-2.
72
These finding are relevant, as the limiting length of a polymer is dependent on the polymer’s tensile
strength.119 As free radicals are capable of lowering the tensile strength of the polymer, this implies
that degradation to shorter chains is possible in the presence of free radicals. The analysis presented
here can be offered as an explanation for observations such as those by Koda where suppression
of radical formation decreases the limiting length of the polymer,106 and suggest that new strategies
in polymer degradation are possible by leveraging the synergy between mechanochemistry and
radical attack.
73
Chapter 5: Conclusions and Final Thoughts
5.1 Research Summary
Despite the rugged, mottled nature of the potential energy surface, only a handful of chemical
states determine the thermodynamics and kinetics of a given chemical reaction. The central
promise of computational chemistry is its ability to both identify and evaluate these key chemical
states. Some of the chapters in this work have mainly been focused on key state identification
(Chapters 2, 3), whereas other chapters have focused on understanding and evaluating key states
(Chapter 4). As demonstrated, both processes provide useful insights for further reaction
development.
In Chapter 2, the mechanism of a nickel-catalyzed three-component coupling reaction of an
aldehyde, alkyne, and enoate is explored. Prior work on the related reductive [3+2] cycloadditions
suggested that two distinct reaction mechanisms were possible, either an aldol-first mechanism
involving a 7-membered metallacycle,50 or a ketene-first mechanism involving a ketene
intermediate.51 As both mechanisms had experimental support for related reactions, the actual
nature of the studied three-component coupling remained ambiguous. Computational studies
provided value, then, because the mechanism of the specific reaction of interest could be directly
interrogated. It was found that the aldol-first and ketene-first pathways were both feasible (Figure
5-1. A summary of Chapter 2. Two mechanisms for the three-component coupling reaction were found to be plausible.
The selectivity for a specific mechanism appears to be affected by the placement of a methyl group at different
positions of the enoate.Figure 5-1), but alkoxide elimination in the ketene-first regime is fast enough
74
to outcompete metallacycle isomerization, meaning that a ketene-first mechanism appears to be
more likely. However, the substitution pattern of the enoate appears to play a role in the choice of
mechanism, as in α-
75
substituted enoates, ketene elimination is much more difficult, due to the steric encumbrance
provided by a group in the α-position. With α-substituted enoates, metallacycle isomerization is
now faster than ketene elimination, which can explain the experimental observation of a linear side
product in only α-substituted enoates, that implicates the existence of a 7-membered metallacycle.
Overall, while the ketene-first pathway was found to be generally favored in the study, it exists in
a precarious balance with an aldol-first mechanism, and as the experience with α-substituted
enoates shows, small changes are capable of changing the preferred mechanism of the reaction.
This work suggests that a similar balance may exist with other reductive [3+2] cycloaddition
reactions, which, as it eventually turned out, includes the activation mechanism of fumarate
catalysts detailed in Chapter 3.
Figure 5-1. A summary of Chapter 2. Two mechanisms for the three-component coupling reaction were found to be
plausible. The selectivity for a specific mechanism appears to be affected by the placement of a methyl group at
different positions of the enoate.
76
Chapter 3 focused on the development of air-stable nickel(0) NHC (N-heterocyclic carbene) pre-
catalysts, and explaining why competent catalysts could be developed with the NHC IMes, but not
with the NHC BAC. Fumarates were chosen as a stabilizing ligand, as they were already known
to be air-stable,83 and it was thought that they could be tuned to become more reactive (Figure 5-2,
A). A series of air-stable fumarate catalysts were developed that could catalyze the reductive
coupling of an alkyne with an aldehyde. While it was originally believed that the activation
mechanism of the fumarate catalysts involved the dissociation of both fumarate ligands,
computational analysis of the binding energies of those catalysts determined that such an activation
mechanism is unlikely (Figure 5-2, B). Even the weakest bound fumarate complex studied had a
binding energy of at least 13.8 kcal/mol, indicating that the fumarate catalyst would be expected
to be over 10 billion times slower than a catalyst formed in situ. The high activity of the fumarate
catalysts, coupled with the knowledge that a fumarate could act as a catalyst poison, suggested that
an activation mechanism where the fumarate is consumed must be active (Figure 5-2, C).
Figure 5-2. (A) Original design strategy to develop an air-stable Ni(0) pre-catalyst. (B) No Correlation between
reaction yield and the free energy of ligand exchange was observed. (C) The absence of such a correlation suggests
that a fumarate consumption reaction must be active.
77
Figure 5-3. The insights gained from Chapter 2 explain why complex 3-8-A is active, but complex 3-10-A is not. The
two complexes undergo activation through different mechanisms. 3-8-A goes through an aldol-first mechanism,
allowing for catalyst activation, but 3-10-A undergoes a ketene-first activation, resulting in a stable ester-ligated
complex.
Leveraging this computational insight, experimentalists were able to isolate the products of the
predicted fumarate consumption mechanism. As the fumarate consumption products were similar
to the products of the three-component coupling reaction detailed in Chapter 2, both the aldol-first
and ketene-first activation mechanisms for IMes and BAC fumarate complexes were investigated.
Like the previous case, mechanism selectivity appeared to be driven by barrier for ketene
elimination (Figure 5-3). For IMes complex 3-8-A, the barrier for ketene elimination is large,
allowing the catalyst to undergo activation through an aldol-first mechanism. However, ketene
elimination is facile for BAC catalyst 3-10-A, suggesting a ketene-first mechanism. This
difference proves to be critical, as the presence of a chelating ester moiety means that the BAC
catalyst can form a highly-stable carbocyclic complex, trapping the catalyst. However, the IMes
catalyst never gets trapped as a highly stabilized species, allowing for the catalyst to activate.
Through the investigating the mechanism of the activation process with computational chemistry,
our understanding of the fumarate catalyst was revolutionized. Applying this insight, preliminary
78
studies in changing the fumarate catalyst to prefer an aldol-first activation path over a ketene-first
activation path provide a direction for the future.
Figure 5-4. A summary of Chapter 4. (A) Radical abstraction imparts a significant change in the enthalpy of bond
scission. (B) The barrier for bond scission in PATH-1 and PATH-2. (C) Differences in the geometries of key states
in PATH-1 and PATH-2. (D) We can explain the differences in behavior between PATH-1 and PATH-2 to be due to
the changes in the curvature of the potential energy surfaces of the two processes.
In Chapter 4, the effect of radical abstraction on the force-enabled bond scission of poly(acrylic
acid) was investigated. Radical abstraction was found to reduce the enthalpy of bond scission by
78.5 kcal/mol, from 92.7 kcal/mol (PATH-1, no radical abstraction) to 14.2 kcal/mol (PATH-2,
with radical abstraction) (Figure 5-4, A). By treating the C-C bond as a Morse oscillator, and
assuming bond scission occurs when no barrier exists for it on the potential energy surface, a crude
estimation of the change in tensile strength suggests that radical attack reduces the tensile strength
of PAA from 6.6 nN to 2.6 nN. Using transition state searching methods recently developed in the
Zimmerman group,96 the transition states of bond scission under force were determined for PATH-
1 and PATH-2. PATH-2 was found to generally have a lower barrier for bond scission, the barrier
79
for bond scission in PATH-2 decreased with increasing applied force compared to PATH-1. Using
the linear relationship of bond scission barrier with applied force, effective tensile strengths in
PATH-1 and PATH-2 were calculated to be 4.7 and 2.5 nN, respectively (Figure 5-4, B).
Additionally, the rationale for how force affects the barrier for bond scission was postulated to be
different in both PATH-1 and PATH-2. In PATH-1, the geometries of the starting structures and
transition states of bond scission were found to change substantially upon application of applied
force, whereas geometric distortions in PATH-2 under force are fairly minimal (Figure 5-4, C).
The large geometric distortions under force, pushing the starting structure and transition state
closer together, can rationalize the decrease in bond dissociation energy in PATH-1. The lack of
distortion in PATH-2, on the other hand, can be explained by the energy of applied force, the
energetic benefit of bond lengthening in the transition state under force. The difference in behavior
between PATH-1 and PATH-2 can also be explained as a consequence of the difference in the
curvature of their respective PESs (Figure 5-4, D). The insights discovered in this chapter suggest
a mechanism of synergy between radical attack and application of tensile force, and may aid in the
development of new depolymerization technology.
5.2 Possible Future Directions for the Material Studied in This Work
Chapters 2 and 3 were mainly focused on the identification of the key states involved in the three-
component coupling reaction, or fumarate catalyst activation, rather than understanding their
nature. Now that metallacycle isomerization and ketene elimination have been identified as key
states, it may be a worthwhile endeavor to try to better understand what factors are capable of
stabilizing and destabilizing them. Tools such as energy decomposition analysis,143 orbital
analysis,144 or distortion-interaction analysis145,146 are all possible means of calculating the impact
of specific features on the selectivity between an aldol-first or a ketene-first reaction. In addition
80
to directly computing the effects of specific descriptors, selectivity-determining features could also
be found through statistical analysis.147
While identifying the features that determine mechanism selectivity for the reactions studied in
Chapters 2 and 3 would be of academic interest, the practical interest of such an inquiry would be
in the development of new pre-catalysts. Smaller NHCs represent an attractive target for pre-
catalyst development, as they have been more unreliable in our hands in in situ procedures. The
preliminary computational work to identify an active BAC fumarate catalyst has already yielded
several candidates of interest, and the relatively minor amount of work required to yield those
results suggests that future attempts with BAC and other NHCs will prove to be similarly facile.
Additionally, the computational analysis described in this work have provided multiple hypothesis
that can be easily proven or disproven through experimental work. For instance, in Chapter 3, the
failure of a BAC fumarate catalyst to activate is hypothesized to be due to its proclivity to become
trapped as an organometallic carbocyclic compound. In theory, this species, or species derived
from it, should be isolable in experiment. The success of such an experiment would provide direct
evidence that complexes such as 3-10-A undergoes a ketene-first activation process, but get
trapped in the process. Such a finding would give credence to the approach of developing fumarate
catalysts that go through an aldol-first activation pathway.
Chapter 4 provides many hypotheses that need to be tested as well. For instance, AFM experiments
to test the effect of radical abstraction on tensile strength would directly confirm the central
assertion of Chapter 4. At the time of writing, such an experiment is being actively researched in
the McNeil group. Additionally, calculations of the rate of bond scission through PATH-1 and
PATH-2 give an estimation on the ratio of limiting length expected during the sonication of
poly(acrylic acid) in the presence and the absence of free radicals. This should be directly
81
measurable, either through the use of radical quenching reagents to inhibit the action of any
radicals generated in solution,106 or through the introduction of a radical generating source such as
Fenton’s reagent.110 As computation provides a quantitative prediction of the expected ratio of
limiting lengths, such an experiment would be a useful barometer for our understanding of the role
of radicals in the sonication process.
5.3 On the Frailty of Human Understanding
In a famous philosophy paper, Edmund Gettier attacked the notion that “justified belief”, i.e. the
existence of supporting evidence for a belief, is sufficient to constitute knowledge.148 Gettier
provides counterexamples, where the justification for an individual’s belief is based on a flawed
premise that makes a successful prediction by coincidence, creating the illusion that the
individual’s belief is knowledgeable. While the original “Gettier problem” consisted of a contrived
example concerning the prediction of employment based on the applicant’s pocket’s contents, real-
world examples of Gettier problems are not uncommon in the research process.
For instance, the initial stages of catalyst design in Chapter 3 played out exactly like a Gettier
problem. The original set of IMes fumarate complexes were designed under the false premise that
catalyst activation occurs through a dissociative mechanism. The fumarates were chosen for their
perceived lack of binding affinity, due to their enhanced steric bulk as compared to the original
methyl substrates used by Cavell.83 When the synthesized catalysts were found to be productive,
the result was originally interpreted as a justification for a dissociative mechanism. But that success
was coincidental. The subsequent computational work detailed in this chapter demonstrated that
in order for the catalyst to activate, rather than simply dissociate, the fumarate needed to be
destroyed. We had originally believed in a wrong mechanism, despite making a successful
82
prediction that provided justification for our initial beliefs. Our initial success was not due to our
knowledge of catalyst activation, but due to random chance.
Even the most carefully justified models can fail to capture the entire picture. In reporting the
nickel-catalyzed reductive [3+2] cycloaddition of enoates and alkynes, Montgomery50 and
Ogoshi51 detail distinctly different mechanisms for the formation of product, and both groups
provided solid experimental evidence for their assertions. In the analysis in Chapter 2, both
mechanisms prove to be viable, and the selectivity between the two mechanisms is easily shifted
by small perturbations. How often does one consider the possibility that two slightly different
substrates can react with the same catalyst to make the same corresponding product, but will go
through completely different mechanisms? How different would our understanding of [3+2]
reductive cycloadditions be, if only one set of mechanistic studies was published, rather than two?
5.4 On the Symbiosis Between Theory and Experiment
What is instructive, then, is how falsely held beliefs can be dispelled with a new perspective. For
instance, in Chapter 3, computational analysis was able to propose a different mechanism of
catalyst activation through the calculation of binding energies. Computational chemists are well
equipped to interrogate specific queries, but are less able to answer more general questions. While
analysis of the binding energies of fumarate clearly demonstrated that some activation mechanism
occurred, which consumed the fumarate, that analysis did not indicate what kind of reaction was
occurring. Despite months of work, computational efforts to identify the mechanism of fumarate
consumption were fruitless, and that question was only resolved once some of the products of
fumarate consumption were ultimately isolated experimentally. General queries, such as
determining the result of a given reaction, are much more easily answered through experiment than
through computation.
83
In short, the strengths and deficiencies of experiment and computation naturally complement each
other, and combined together they can enjoy a symbiotic relationship. Such a relationship is
displayed throughout Chapter 3, as the chapter consists of a series of iterations where the
experimentalists feed insight to theoreticians, and vice versa. It is impossible to talk about the
contributions from one side without mentioning the other. The experimentalists would be lost,
chasing after the wrong mechanism of catalyst activation, absent a computational investigation.
The theoretician would be stuck, unable to process all possible methods of fumarate consumption,
without experimental isolation of the products of fumarate consumption. Computational chemistry
has always needed the support of experimentalists, as they ultimately need to test in the real world
the predictions made in simulation. But, as Chapter 3 demonstrates, the growth of computing
power and the development of better tools have made computational chemistry powerful enough
that perhaps the experimentalists need the theoreticians as well.
84
Appendix
A.1 Computational Details for Chapters 2 and 3
Density functional calculations were performed using Q-Chem 3.1.0.0149 for geometry
optimization and frequency calculations, and ORCA 4.0.0.2150 for single point calculations. All
geometries for intermediates and transition states were optimized using the ωB97X density
functional13 and 6-31G(d) basis set.151,152 Energies were refined by applying the ωB97X-D3
density functional11 with the cc-pVTZ basis153,154 and the SMD implicit solvent model155 with
toluene as the solvent (𝜖 2.4) in Chapter 2, or tetrahydrofuran as the solvent in Chapter 3 (𝜖
7.25). Transition state geometries and minimum energy reaction paths were found using the single-
26 and double-ended24,25 growing string methods. Found transition states were subsequently re-
optimized after the initial search. All energies listed are Gibbs free energies with enthalpy and
entropy corrections at 363 K for Chapter 2, or 298 K for Chapter 3. Entropy corrections were
scaled to 50% to account for the difference in entropy between the gas and solvated phases.156 The
effects of low frequency oscillations were reassigned to 50 cm-1 to prevent the highly anharmonic
vibrations from overly influencing the free energy. All intermediates and transition states were
confirmed to have the appropriate number of imaginary frequencies: one for transition states, and
none for intermediates. All geometry optimizations, frequency calculations, were performed with
an SCF convergence tolerance of 10-6. Single point calculations were performed with an SCF
convergence tolerance of 10-8.
85
A.2 Raw Energies of Structures in Chapter 3
The values used to calculate the relative energies reported for the activation IMes complex 3-8-A
are reported in Table A-1. The values used to calculate the relative energies reported for the
activation BAC complex 3-10-A are reported in Table A-2. The values for the small molecules
used for energy balance in to investigate the pathways of both complexes are given in Table A-3.
The values used to calculate the relative energies of ketene elimination and metallacycle
isomerization for various BAC complexes are given in Table A-4.
Electronic Energy
Zero-Point
Correction Entropy
Complex In hartrees In kcal/mol In cal/mol
IMes-I -3777.07273088773 573.922 280.182
IMes-II -3777.06117723177 573.143 283.499
IMes-TS-II-A -3777.04514633182 572.894 288.034
IMes-III-A -3777.05906179391 574.141 279.708
IMes-TS-III-A -3777.04332245166 570.850 290.026
IMes-TS-II-B -3777.03518980009 572.965 284.492
IMes-III-B -3777.04967194343 571.860 288.283
IMes-IV-A -3777.05529741875 572.734 291.940
IMes-V-A -4221.92540429087 643.799 322.100
IMes-TS-V-A -4221.91122019430 645.019 315.399
IMes-VI-A -4221.93699056449 646.246 318.960
IMes-VI-A-THF -4454.43215241548 725.763 344.347
IMes-TS-VI-A -4631.81573109319 729.845 340.705
IMes-VII-A -4631.84843879111 728.486 353.729
IMes-VIII-A -4631.86712697850 727.700 354.000
IMes-TS-VIII-Z -4631.81904752115 725.879 360.842
IMes-IX-Z -4631.88041138076 731.512 346.623
IMes-TS-VIII-A -4631.83086136393 727.761 348.589
IMes-IX-A -4631.88910809406 728.400 354.700 Table A-1. Energetic values used to calculate relative energies in the activation pathway of IMes catalyst 3-8-A.
86
Electronic Energy
Zero-Point
Correction Entropy
Complex In hartrees In kcal/mol In cal/mol
BAC-I -3550.76343327492 578.960 279.691
BAC-II -3550.75674927357 577.728 280.608
BAC-TS-II-A -3550.74925510619 578.010 280.754
BAC-III-A -3550.75561877717 578.742 281.754
BAC-TS-III-A -3550.72892166746 577.582 284.884
BAC-IV-A -3550.74538535549 579.194 280.742
BAC-TS-II-B -3550.73607756652 576.436 287.907
BAC-III-B -3550.75087524428 576.949 286.110
BAC-TS-III-B -3550.74774549022 576.884 284.392
BAC-IV-B -3550.79413870639 579.320 274.808
BAC-TS-IV-B -3960.65643023093 660.998 314.962
BAC-V-B -3205.14638400882 500.812 246.156
BAC-TS-V-B -3205.09188866902 500.374 249.289
BAC-VI-B -3205.15075011543 501.862 248.227 Table A-2. Energetic values used to calculate relative energies in the activation pathway of BAC catalyst 3-10-A.
Electronic Energy
Zero-Point
Correction Entropy
Structure In hartrees In kcal/mol In cal/mol
4-Fluorobenzaldehyde -444.849789364677 69.976 87.066
Tetrahydrofuran -232.476787942352 78.456 73.154
Trimethylsilane -409.886233904854 81.594 81.022
Trimethyl(o-tolyloxy)silane -755.554325411818 159.348 120.207 Table A-3. Energetic values of small molecules used in the calculations of the activation pathways of both 3-8-A
and 3-10-A.
87
Electronic Energy
Zero-Point
Correction Entropy
Step Fumarate In hartrees In kcal/mol In cal/mol
Ref
eren
ce S
truct
ure
(BA
C-I
)
B -3245.91786662683 545.782 262.207
C -3708.05413664578 653.753 307.495
D -3786.65666774105 691.481 310.894
E -3701.18954413056 584.265 291.184
F -3701.18423696250 584.668 291.281
G -3927.93003945740 600.994 302.797
H -3472.12061691597 541.119 266.985
I -3088.62438412179 470.217 241.505
J -3550.75595586925 577.783 283.021
K -4012.88691971857 689.340 318.855
L -4146.30809886054 551.998 295.784
M -3786.65666774105 691.481 310.894
Ket
ene
Eli
min
atio
n
(BA
C-T
S-I
I-B
)
B -3245.8741121607 543.421 266.582
C -3708.0161805980 652.128 307.922
D -3786.6275131312 690.863 313.821
E -3701.1698962121 584.891 293.175
F -3701.1673810115 584.509 289.833
G -3927.9066423323 600.542 312.494
H -3472.0938845943 539.281 274.493
I -3088.5819107818 468.205 246.462
J -3550.7159490670 577.768 286.908
K -4012.8532280731 687.520 321.935
L -4146.2850054481 550.963 303.283
M -3786.6275131312 690.863 313.821
Met
alla
cycl
e Is
om
eriz
atio
n
(BA
C-T
S-I
II-A
)
B -3245.8774350755 544.866 269.403
C -3708.0145582864 652.361 315.516
D -3786.6276568147 691.517 313.872
E -3701.1539418405 585.213 296.583
F -3701.1496653065 584.945 295.110
G -3927.8960549849 601.138 312.019
H -3472.0850514741 540.094 274.022
I -3088.5839657167 469.529 248.021
J -3550.7187597531 579.036 289.319
K -4012.8534021955 688.316 323.586
L -4146.2741266509 550.520 308.544
M -3786.6276568147 691.517 313.872 Table A-4. Energetic values used in the comparison of ketene elimination with metallacycle isomerization of BAC
complexes using different fumarates.
88
A.3 Methodology Used in Chapter 4
To capture the behavior of PAA, an isotactic tetramer was used as a model system (1) (Figure
A-1). The effects of radical abstraction were modeled using the same tetramer, minus an α-
hydrogen next to a central carboxyl group (2) (Figure A-1). Conformers for 1 were generated using
the Confab tool130 in Open Babel.131 8 unique conformers were identified. Conformers for 2 were
generated by abstracting the α-hydrogen from each of the conformers of 1.
Figure A-1. Model PAA systems used in this study.
As hydrogen bonding is known to affect the heat of polymerization of protic polymers such as
PAA,132 and to ensure that the conformers used in this study are consistent with aqueous solvation,
explicit water solvation was used. For each conformer of 1 and 2, the system was surrounded by a
6 Å water shell containing 260 water molecules. Molecular dynamics (MD) simulations were used
to create a series of snapshots of the tetramer in an aqueous environment. These simulations were
carried out using the TINKER package, version 8.2.157 10 ns of NVT molecular dynamics was
simulated with a 1 fs timestep using the CHARMM 2217,18 forcefield with an Andersen thermostat
and a modified Beeman integrator. Custom parameters were created to model the α-radical in 2
(see Section A.4). Water was treated using the TIP3P model. Electrostatic interactions were treated
using Ewald summation, with a cutoff value of 7 Å. All other nonbonded interactions were treated
using a cutoff of 8 Å. The entire system was simulated in a 23.418 Å by 19.166 Å by 18.613 Å
rectangular cuboid box with periodic boundary conditions. After 2 ns of equilibration, snapshots
were taken every 100 fs. For both model systems (1 and 2), the snapshots from each conformer
89
was combined into a single pool of 640 snapshots. The conformers were then relaxed using the
OPTIMIZE function in TINKER.
The geometry of selected snapshots was then re-optimized using a quantum mechanical/molecular
mechanical method (QM/MM). For the QM/MM optimizations, the QM region was treated using
the B3LYP functional12 with the 6-31G(d)151 basis. Edge water molecules were fixed in place. The
MM region was treated using the same CHARMM 2217,18 forcefield also used in the MD
simulations. The Janus model was used for electronic embedding.16,19 Optimizations were
performed with an SCF convergence tolerance 10-6.
Not all of the collected snapshots from the MD simulations were used. For the QM/MM re-
optimization of 1, 200 of the 640 snapshots were used, taken at regular intervals. For 2, snapshots
were screened for those that had a proper alignment of the middle carboxylic acid with the α-
radical. For a β-scission event to occur, the radical must overlap with the scissile bond to
accommodate formation of a new pi bond.158 This was defined as being within 20° of being anti-
periplanar, or 30° of being syn-periplanar with the middle carboxylic acid (see Figure A-1). After
screening all 640 snapshots of 2, 121 were used for QM/MM optimizations. A flowchart for the
entire process is shown in Figure A-2.
Figure A-2. Flowchart for QM/MM optimization and bond scission.
90
After optimizing the geometry of the snapshots, the scissile bond (shown in red, Figure A-2) was
cleaved by applying a stretching force of 10 nN between the two atoms of the scissile bond using
the EFEI (external force explicitly included) method.133 After bond scission, subsequent re-
optimization yielded two PAA dimers (referred to as dimer+dimer snapshots).
As Figure A-2 details, in the case of no radical activation (1), of the 200 snapshots used, 178 were
successfully optimized using the QM/MM method, 170 were then successfully broken, and 166
snapshots were successfully re-optimized as dimer+dimer snapshots. For the no activation case,
dimer+dimer optimization was performed on the triplet surface to prevent recombination, and then
singlepoint energies on the singlet surface were then calculated. In the case of radical activation
(2), of the 121 snapshots used, 103 were successfully optimized using the QM/MM method, 65
were successfully broken, and 62 of the dimer+dimer snapshots were successfully reoptimized.
The enthalpy of bond scission was determined by comparing the total energy of each dimer+dimer
snapshots to the tetramer snapshot it came from. By averaging the difference in energy for each
set of snapshots, a value for the enthalpy of bond scission could be obtained. In the no activation
case (1), the 166 dimer+dimer snapshots were compared to their original tetramer snapshot. The
same analysis was made for the 62 dimer+dimer snapshots in the radical activation case. For all
optimized tetramers in the no activation and radical activation regimes, partial hessian vibrational
analysis134 was performed on the structures absent any explicit water. These values were averaged
to yield the force constant of the scissile bond (shown in red, Figure A-2).
Using the reactant geometry and a C-C scission bond-dissociation coordinate, the single-ended
growing string method allows for the identification of the transition state (TS) of a reaction,
without prior guessing of the structure of the TS.24 Roessler and Zimmerman described a such a
method that includes force biasing (F-GSM).96 Herein, double-ended F-GSM is used to identify
91
the structure of the TS of bond scission of 1, and single-ended F-GSM is used to identify the
structure of the TS of bond scission of 2. A double-ended method was necessary to investigate 1
to calculate a driving coordinate that was sufficient to overcome the large bond dissociation energy
of the reaction. Force was applied at the ends of the tetramer unit, shown in Figure A-3. Due to the
complexity of the system, a tetrameric system was the largest polymer analogue that could be
produce useful data in a reasonable timeframe. Boulatov has previously shown that any effects of
the length of the model system would have a maximum error of ~4 kcal/mol, but that decreases
sharply with increasing system size.159
Figure A-3. Points where force is applied on compounds 1 and 2. The scissile bonds are shown in red.
During ultrasonic depolymerization, the polymer strand will undergo a coil-stretch transition prior
to scission.91 This transition was found to have a confounding effect on the transition state energies
obtained. To resolve this hysteresis problem, structures were optimized at a high level of force,
and then relaxed to their optimized geometries at the desired force level.96
To optimize structures prior to the transition state searching, snapshots were re-optimized with
force applied using the EFEI method.133 For the scission of 1, 129 snapshots of 1 were optimized
at 6 nN, and then re-optimized at forces ranging from 3 to 5 nN. At these force ranges, the bond
scission is sufficiently exothermic for the strings to have an energy profile consistent with having
a transition state. Their corresponding dimer+dimer snapshots were similarly optimized, except
that the procedure was performed on the triplet surface with the scissile atoms frozen. The
tetramer/dimer+dimer pairs were then used as start and end structures to find the transition state
92
of bond scission using double-ended F-GSM. The resulting transition state energies relative to the
starting structure was then averaged to yield a transition state energy at a given force value. A
flowchart from this process is given in Figure A-4.
Figure A-4. Flowchart for identifying the transition state of bond scission for compound 1.
For the scission of 2, tetramers were extended using a force of 6 nN, and then relaxed to their
optimized geometries at the desired levels of force. This ensured that the polymer strand remained
straight, and avoided including the energy of polymer uncoiling in the transition state energy. The
optimized structures were then used as starting points using single-ended F-GSM. The resulting
transition state energies relative to the starting structure was then averaged to yield a transition
state energy at a given force value. A flowchart from this process is given in Figure A-5.
Figure A-5. Flowchart for identifying the transition state of bond scission for compound 2.
93
In order to effectively interrogate the depolymerization of PAA under aqueous conditions, it is
necessary to find a model that yields suitably accurate energetic information. The polymerization
of acrylic acid under aqueous conditions is known to have an enthalpy of polymerization of 18.5
kcal/mol.139 Given that the heat of polymerization of protic monomers is known to be affected by
the hydrogen-bonding ability of the environment, we explored the use of a QM/MM system with
explicit water molecules that were simulated using molecular mechanics. Using a QM/MM method
with explicit water atoms, the value for the enthalpy of polymerization was found to be 15.9
kcal/mol.
94
A.4 Radical Parameters Used in the Molecular Dynamics Simulations in Chapter 4
The following molecular mechanics parameters were used to simulate the radical carbon in
compound 2 for dynamics simulations performed in Chapter 4. They are designed to be used in
conjunction with the CHARMM 22 parameter file (“charmm22.prm”) included in TINKER,
version 8.2.157
atom 999 99 RAD "Radical" 6 12.011 3
vdw 99 2.0900 -0.0680
charge 999 -0.0900
bond 99 42 300.00 1.4800
bond 99 13 365.00 1.5020
bond 99 14 365.00 1.5020
bond 99 1 36.50 1.1000
bond 99 12 440.00 1.4890
angle 42 99 14 65.00 123.50
angle 99 14 13 32.00 112.20
angle 99 14 1 45.00 111.50
angle 14 99 1 40.00 116.00
angle 99 42 52 75.00 126.00
angle 99 42 35 55.00 110.50
angle 42 99 1 32.00 122.00
angle 12 99 14 65.00 123.50
angle 1 99 12 52.00 119.50
angle 14 99 14 27.00 114.00
torsion 14 99 42 52 1.4000 180.00 2
torsion 14 99 42 35 1.4000 180.00 2
torsion 42 99 14 13 0.3000 0.00 3
torsion 42 99 14 1 0.0000 0.00 3
torsion 99 42 35 3 2.0500 180.000 2
torsion 42 13 14 99 0.2000 0.00 3
torsion 15 13 14 99 0.2000 0.00 3
torsion 14 13 14 99 0.2000 0.00 3
torsion 1 13 14 99 0.2000 0.00 3
torsion 42 99 52 35 53.0000 0.00 0
torsion 14 13 14 99 0.2000 0.00 3
torsion 13 14 99 1 0.0000 0.00 3
torsion 1 99 14 1 0.0000 0.00 3
torsion 1 99 42 52 0.0000 180.00 2
torsion 1 99 42 35 0.0000 180.00 2
torsion 13 14 99 12 0.2000 0.00 3
torsion 12 13 14 99 0.2000 0.00 3
torsion 12 99 14 1 0.0000 180.00 3
torsion 14 99 14 1 0.0000 0.00 3
torsion 13 14 99 14 8.5000 180.0
95
A.5 Data Used to Calculate the Tensile Strength and Rates of Bond Scission in Chapter 4
To calculate the tensile strength using the Morse method, the force constant of the scissile bond,
κ, as well as the energy of bond dissociation, E0 need to be calculated. Averages of those values
are listed in Table A-5 and Table A-6.
Avg. E0 (kcal/mol) Std. Err. Std. Dev. N
PATH-1 92.722 0.6126 7.8925 166
PATH-2 14.199 0.7763 6.1126 62 Table A-5. Average calculated bond dissociation energy values in PATH-1 and PATH-2.
Avg. κ (nN/Å) Std. Err. Std. Dev. N
PATH-1 54.0700 0.076961 1.032538 180
PATH-2 54.0471 0.096577 0.970591 101 Table A-6. Average calculated force constants in PATH-1 and PATH-2.
Table A-7 tabulates the average barriers for bond scission in PATH-1 and PATH-2.
Force in nN Avg. ΔH‡ in kcal/mol Std. Err. Std. Dev. N
PA
TH
-1 3 37.212 2.109 15.644 55
3.5 30.568 2.547 18.013 50
4 28.551 2.101 16.546 62
4.5 21.221 1.476 10.440 50
5 19.629 1.805 13.388 55
PA
TH
-2
0 30.236 0.637 3.824 36
1 27.377 0.676 4.585 46
2 24.200 0.767 5.426 50
3 19.959 0.528 4.288 66
4 15.708 0.699 5.326 58
5 10.301 0.473 3.728 62 Table A-7. The average barriers for bond scission in PATH-1 and PATH-2.
96
A.6 Tabulation of the Raw Geometric Data in Chapter 4
The average end-to-end and scissile bond distances of 1, 2, TS-1, and TS-2 are given in Table
A-8. All other geometric analyses performed in Chapter 4 can be derived from these values.
Distances in Å
End-to-End Scissile Bond Force in nN Mean Std. Dev. Mean Std. Dev. N
1
3 9.7764 0.0342 1.5809 0.0023 50
3.5 9.9637 0.0266 1.5918 0.0025 55
4 10.0942 0.0232 1.5934 0.0023 50
4.5 10.2883 0.0239 1.5977 0.0024 62
5 10.4158 0.0234 1.6079 0.0025 55
TS
-1
3 10.9265 0.0625 2.6332 0.0644 50
3.5 10.9073 0.0622 2.4355 0.0654 55
4 10.8884 0.0526 2.3239 0.0609 50
4.5 11.0082 0.0543 2.2566 0.0625 62
5 11.0116 0.0476 2.1550 0.0591 55
2
0 8.7612 0.1050 1.5608 0.0013 36
1 9.5658 0.0532 1.5675 0.0014 46
2 9.9411 0.0407 1.5748 0.0014 50
3 10.2539 0.0263 1.5828 0.0013 66
4 10.5073 0.0211 1.5918 0.0014 58
5 10.6916 0.0220 1.6018 0.0014 62
TS
-2
0 8.9982 0.1097 2.3756 0.0167 36
1 9.8525 0.0584 2.3008 0.0132 46
2 10.2824 0.0499 2.2657 0.0192 50
3 10.5872 0.0314 2.2585 0.0108 66
4 10.8804 0.0283 2.2614 0.0133 58
5 11.0357 0.0287 2.2306 0.0120 62
Table A-8. The average end-to-end and scissile bond distances in 1, 2, TS-1, and TS-2.
97
A.7 Raw Data and Parameters Used in the Mathematical Model in Chapter 4
The parameters used in the mathematical modelling of PATH-1 and PATH-2 in Chapter 4 are
detailed in Table A-9.
PATH-1: 𝐸 𝐷(1 − 𝑒𝛼(𝑟−𝑟𝑒))2 − 𝐹𝑟 PATH-2: 𝐸 𝐴𝑟4 − 𝐵𝑟2 𝐶 − 𝐹𝑟
Parameter Value Parameter Value
𝐷 93 A 71
𝛼 2.63 B 93
re 0.8 C 30.8 Table A-9. Parameters used for mathematical modeling in Chapter 4.
The datapoints for the change in transition state energy for the mathematical models of PATH-1
and PATH-2 are shown in Table A-10.
Value for ∆𝐻‡
Force
PATH-1
(Morse)
PATH-2
(Quartic)
0 93.000 30.454
1 90.266 29.649
2 88.061 28.852
3 86.056 28.063
4 84.182 27.282
5 82.405 26.509
6 80.707 25.745
7 79.074 24.989
8 77.497 24.241
9 75.969 23.501
10 74.486 22.770
11 73.042 22.047
12 71.634 21.333
13 70.260 20.628
14 68.917 19.931
15 67.603 19.242
16 66.315 18.563
17 65.054 17.892
18 63.816 17.230
19 62.601 16.577
20 61.408 15.933 Table A-10.The change in the transition state energy of the mathematical models of PATH-1 and PATH-2.
98
The datapoints for the displacement of the location of the transition state are shown in Table
A-11.
Displacement of Transition
State From F=1
Force
PATH-1
(Morse)
PATH-2
(Quartic)
1 0.0000 0.0000
2 -0.2643 -0.0054
3 -0.4193 -0.0108
4 -0.5295 -0.0161
5 -0.6151 -0.0215
6 -0.6852 -0.0269
7 -0.7447 -0.0323
8 -0.7963 -0.0378
9 -0.8419 -0.0432
10 -0.8828 -0.0486
11 -0.9198 -0.0541
12 -0.9537 -0.0596
13 -0.9850 -0.0650
14 -1.0140 -0.0706
15 -1.0411 -0.0761
16 -1.0665 -0.0817
17 -1.0904 -0.0872
18 -1.1131 -0.0928
19 -1.1345 -0.0985
20 -1.1549 -0.1042 Table A-11. Displacement of the position of the transition state in the mathematical models of PATH-1 and PATH-
2.
99
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